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Dissertations / Theses on the topic 'Ordinary fourth-order differential equations'
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1
Woods, Patrick Daniel. "Localisation in reversible fourth-order ordinary differential equations." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299269.
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Jenab, Bita. "Asymptotic theory of second-order nonlinear ordinary differential equations." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24690.
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The asymptotic behaviour of nonoscillatory solutions of second order nonlinear ordinary differential equations is studied. Necessary and sufficient conditions are given for the existence of positive solutions with specified asymptotic behaviour at infinity. Existence of nonoscillatory
solutions is established using the Schauder-Tychonoff fixed point theorem. Techniques such as factorization of linear disconjugate operators are employed to reveal the similar nature of asymptotic solutions of nonlinear
differential equations to that of linear equations. Some examples illustrating the asymptotic theory of ordinary differential equations are given.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate
3
Sun, Xun. "Twin solutions of even order boundary value problems for ordinary differential equations and finite difference equations." [Huntington, WV : Marshall University Libraries], 2009. http://www.marshall.edu/etd/descript.asp?ref=1014.
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Boutayeb, Abdesslam. "Numerical methods for high-order ordinary differential equations with applications to eigenvalue problems." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278244.
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Esposito, Elena. "Numerical treatment of special second order ordinary differential equations: general and exponentially fitted methods." Doctoral thesis, Universita degli studi di Salerno, 2012. http://hdl.handle.net/10556/292.
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2010 - 2011<br>The aim of this research is the construction and the analysis of new families of numerical
methods for the integration of special second order Ordinary Differential Equations
(ODEs). The modeling of continuous time dynamical systems using second order ODEs
is widely used in many elds of applications, as celestial mechanics, seismology, molecular
dynamics, or in the semidiscretisation of partial differential equations (which leads to
high dimensional systems and stiffness). Although the numerical treatment of this problem
has been widely discussed in the literature, the interest in this area is still vivid,
because such equations generally exhibit typical problems (e.g. stiffness, metastability,
periodicity, high oscillations), which must efficiently be overcome by using suitable
numerical integrators. The purpose of this research is twofold: on the one hand to construct
a general family of numerical methods for special second order ODEs of the type
y00 = f(y(t)), in order to provide an unifying approach for the analysis of the properties
of consistency, zero-stability and convergence; on the other hand to derive special
purpose methods, that follow the oscillatory or periodic behaviour of the solution of the
problem...[edited by author]<br>X n. s.
6
Gray, Michael Jeffery Henderson Johnny L. "Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations." Waco, Tex. : Baylor University, 2006. http://hdl.handle.net/2104/4185.
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Koike, Tatsuya. "On the exact WKB analysis of second order linear ordinary differential equations with simple poles." 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/181093.
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Granström, Frida. "Symmetry methods and some nonlinear differential equations : Background and illustrative examples." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-48020.
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Differential equations, in particular the nonlinear ones, are commonly used in formulating most of the fundamental laws of nature as well as many technological problems, among others. This makes the need for methods in finding closed form solutions to such equations all-important. In this thesis we study Lie symmetry methods for some nonlinear ordinary differential equations (ODE). The study focuses on identifying and using the underlying symmetries of the given first order nonlinear ordinary differential equation. An extension of the method to higher order ODE is also discussed. Several illustrative examples are presented.<br>Differentialekvationer, framförallt icke-linjära, används ofta vid formulering av fundamentala naturlagar liksom många tekniska problem. Därmed finns det ett stort behov av metoder där det går att hitta lösningar i sluten form till sådana ekvationer. I det här arbetet studerar vi Lie symmetrimetoder för några icke-linjära ordinära differentialekvationer (ODE). Studien fokuserar på att identifiera och använda de underliggande symmetrierna av den givna första ordningens icke-linjära ordinära differentialekvationen. En utvidgning av metoden till högre ordningens ODE diskuteras också. Ett flertal illustrativa exempel presenteras.
9
Shu, Yupeng. "Numerical Solutions of Generalized Burgers' Equations for Some Incompressible Non-Newtonian Fluids." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2051.
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The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.
10
Yaakub, Abdul Razak Bin. "Computer solution of non-linear integration formula for solving initial value problems." Thesis, Loughborough University, 1996. https://dspace.lboro.ac.uk/2134/25381.
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This thesis is concerned with the numerical solutions of initial value problems with ordinary differential equations and covers single step integration methods. focus is to study the numerical the various aspects of Specifically, its main methods of non-linear integration formula with a variety of means based on the Contraharmonic mean (C.M) (Evans and Yaakub [1995]), the Centroidal mean (C.M) (Yaakub and Evans [1995]) and the Root-Mean-Square (RMS) (Yaakub and Evans [1993]) for solving initial value problems. the applications of the second It includes a study of order C.M method for parallel implementation of extrapolation methods for ordinary differential equations with the ExDaTa schedule by Bahoshy [1992]. Another important topic presented in this thesis is that a fifth order five-stage explicit Runge Kutta method or weighted Runge Kutta formula [Evans and Yaakub [1996]) exists which is contrary to Butcher [1987] and the theorem in Lambert ([1991] ,pp 181). The thesis is organized as follows. An introduction to initial value problems in ordinary differential equations and parallel computers and software in Chapter 1, the basic preliminaries and fundamental concepts in mathematics, an algebraic manipulation package, e.g., Mathematica and basic parallel processing techniques are discussed in Chapter 2. Following in Chapter 3 is a survey of single step methods to solve ordinary differential equations. In this chapter, several single step methods including the Taylor series method, Runge Kutta method and a linear multistep method for non-stiff and stiff problems are also considered. Chapter 4 gives a new Runge Kutta formula for solving initial value problems using the Contraharmonic mean (C.M), the Centroidal mean (C.M) and the Root-MeanSquare (RMS). An error and stability analysis for these variety of means and numerical examples are also presented. Chapter 5 discusses the parallel implementation on the Sequent 8000 parallel computer of the Runge-Kutta contraharmonic mean (C.M) method with extrapolation procedures using explicit assignment scheduling Kutta RK(4, 4) method (EXDATA) strategies. A is introduced and the data task new Rungetheory and analysis of its properties are investigated and compared with the more popular RKF(4,5) method, are given in Chapter 6. Chapter 7 presents a new integration method with error control for the solution of a special class of second order ODEs. In Chapter 8, a new weighted Runge-Kutta fifth order method with 5 stages is introduced. By comparison with the currently recommended RK4 ( 5) Merson and RK5(6) Nystrom methods, the new method gives improved results. Chapter 9 proposes a new fifth order Runge-Kutta type method for solving oscillatory problems by the use of trigonometric polynomial interpolation which extends the earlier work of Gautschi [1961]. An analysis of the convergence and stability of the new method is given with comparison with the standard Runge-Kutta methods. Finally, Chapter 10 summarises and presents conclusions on the topics discussed throughout the thesis.
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Rangelova, Marina. "Error estimation for fourth order partial differential equations." Ann Arbor, Mich. : ProQuest, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3258675.
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Thesis (Ph.D. in Computational and Applied Mathematics)--S.M.U., 2007.<br>Title from PDF title page (viewed Mar. 18, 2008). Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1675. Adviser: Peter Moore. Includes bibliographical references.
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Šustková, Apolena. "Řešení obyčejných diferenciálních rovnic neceločíselného řádu metodou Adomianova rozkladu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445455.
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This master's thesis deals with solving fractional-order ordinary differential equations by the Adomian decomposition method. A part of the work is therefore devoted to the theory of equations containing differential operators of non-integer order, especially the Caputo operator. The next part is devoted to the Adomian decomposition method itself, its properties and implementation in the case of Chen system. The work also deals with bifurcation analysis of this system, both for integer and non-integer case. One of the objectives is to clarify the discrepancy in the literature concerning the fractional-order Chen system, where experiments based on the use of the Adomian decomposition method give different results for certain input parameters compared with numerical methods. The clarification of this discrepancy is based on recent theoretical knowledge in the field of fractional-order differential equations and their systems. The conclusions are supported by numerical experiments, own code implementing the Adomian decomposition method on the Chen system was used.
13
Ma, Ding Henderson Johnny. "Uniqueness implies uniqueness and existence for nonlocal boundary value problems for fourth order differential equations." Waco, Tex. : Baylor University, 2005. http://hdl.handle.net/2104/3577.
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ROMANI, GIULIO. "Positivity and qualitative properties of solutions of fourth-order elliptic equations." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/525734.
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This thesis concerns the study of fourth-order elliptic boundary value problems and, in particular, qualitative properties of solutions. Such problems arise in various fields, from plate theory to conformal geometry and, compared to their second-order counterparts, they present intrinsic difficulties, mainly due to the lack of the maximum principle.
In the first part of the thesis, we study the positivity of solutions in case of Steklov boundary conditions, which are intermediate between Dirichlet and Navier boundary conditions. They naturally appear in the study of the minimizers of the Kirchhoff-Love functional, which represents the energy of a hinged thin and loaded plate in dependence of a parameter. We establish sufficient conditions on the domain to obtain the positivity of the minimizers of the functional. Then, for such domains, we study a generalized version of the functional. Using variational techniques, we investigate existence and positivity of the ground states, as well as their asymptotic behaviour for the relevant values of the parameter.
In the second part of the thesis we establish uniform a-priori bounds for a class of fourth-order semilinear problems in dimension 4 with exponential nonlinearities. We considered both Dirichlet and Navier boundary conditions and we suppose our nonlinearities positive and subcritical. Our arguments combine uniform estimates near the boundary and a blow-up analysis. Finally, by means of the degree theory, we obtain the existence of a positive solution.
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Romani, Giulio. "Positivity and qualitative properties of solutions of fourth-order elliptic equations." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0359/document.
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Cette thèse concerne l'étude de certains problèmes elliptiques d'ordre 4 et, notamment, des propriétés qualitatives des solutions. Ces problèmes apparaissent dans de nombreux domaines, par exemple dans la théorie des plaques et dans la géométrie conforme, et, comparés à leurs homologues du deuxième ordre, ils présentent des difficultés intrinsèques, surtout liées à l'absence de principe de maximum. Premièrement on étudie la positivité des solutions dans le cas des conditions au bord de Steklov, qui sont intermédiaires entre les conditions de Dirichlet et de Navier. Elles apparaissent naturellement dans l'étude des minimiseurs de la fonctionnelle de Kirchhoff-Love, qui représente l'énergie d'une plaque encastrée soumise à l'action d'une force extérieure, en fonction d'un paramètre $\sigma$. On trouve des conditions suffisantes sur le domaine pour que les minimiseurs de la fonctionnelle soient positifs. De plus, pour ces domaines on étudie une version généralisée de la fonctionnelle. En utilisant des techniques variationnelles, on examine l'existence et la positivité des états fondamentaux, ainsi que leur comportement asymptotique pour les valeurs pertinentes de $\sigma$. Dans la deuxième partie de la thèse on établit des estimations uniformes a priori pour des problèmes semi linéaires du quatrième ordre dans $\mathbb R^4$, et donc avec des non linéarités exponentielles. On considère des conditions au bord soit de Dirichlet soit de Navier et on suppose que les non linéarités sont positives et sous-critiques. Nos arguments combinent des estimations uniformes près du bord et une analyse de blow-up. Enfin, en utilisant la théorie du degré, on obtient l'existence d'une solution<br>This thesis concerns the study of fourth-order elliptic boundary value problems and, in particular, qualitative properties of solutions. Such problems arise in various fields, from plate theory to conformal geometry and, compared to their second-order counterparts, they present intrinsic difficulties, mainly due to the lack of the maximum principle. In the first part of the thesis, we study the positivity of solutions in case of Steklov boundary conditions, which are intermediate between Dirichlet and Navier boundary conditions. They naturally appear in the study of the minimizers of the Kirchhoff-Love functional, which represents the energy of a hinged thin and loaded plate in dependence of a parameter $\sigma$. We establish sufficient conditions on the domain to obtain the positivity of the minimizers of the functional. Then, for such domains, we study a generalized version of the functional. Using variational techniques, we investigate existence and positivity of the ground states, as well as their asymptotic behaviour for the relevant values of $\sigma$. In the second part of the thesis we establish uniform a-priori bounds for a class of fourth-order semi linear problems in $\mathbb R^4$, and thus with exponential non linearities. We considered both Dirichlet and Navier boundary conditions and we suppose our non linearities positive and subcritical. Our arguments combine uniform estimates near the boundary and a blow-up analysis. Finally, by means of the degree theory, we obtain the existence of a positive solution
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Marino, Greta. "A-priori estimates for some classes of elliptic problems." Doctoral thesis, Università di Catania, 2019. http://hdl.handle.net/10761/4116.
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L'obiettivo di questa tesi è di studiare alcuni aspetti di un potente strumento ampiamente utilizzato in analisi matematica, che è rappresentato dalle stime a priori. Infatti, le stime a priori hanno un ruolo chiave nella teoria delle equazioni differenziali a derivate parziali e nel calcolo delle variazioni, perché sono intimamente legate all'esistenza di soluzione per un dato problema. Nella tesi vengono presentati tre lavori scritti durante il periodo del dottorato, in ciascuno dei quali vengono utilizzate le stime a priori.
Il primo lavoro, scritto in collaborazione con il Prof. S. Mosconi, riguarda l'esistenza di soluzione per la seguente equazione differenziale ordinaria del quarto ordine (equazione di Swift-Hohenberg), $ u''''+ qu''+ F'(u)= 0$, dove $q$ è un parametro reale e $F$ è una funzione $C^2$, coerciva e quasi-convessa.
Il secondo lavoro, scritto in collaborazione con il prof. P. Winkert, riguarda stime a priori per un problema ellittico in cui gli operatori hanno crescita critica, sia nel dominio che sulla frontiera.
Il terzo lavoro, scritto in collaborazione con i Prof. S.A. Marano e A. Moussaoui, riguarda l'esistenza di soluzione per un sistema ellittico definito in tutto lo spazio $\R^N$, in cui le nonlinearità contengono termini singolari, cioè che possono tendere a $+\infty$ quando la variabile tende a zero.
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Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.
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Doutoramento em Matemática<br>Nesta tese de Doutoramento desenvolve-se principalmente uma abordagem
algébrica à teoria de sistemas de controlo não lineares. No entanto, outros
tópicos são também estudados. Os tópicos tratados são os seguidamente
enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres,
estabilidade de um sistema de corpos rolantes, algoritmos para aritmética
digital, e equações integrais de Fredholm não lineares.
No primeiro e principal tópico estudam-se representações para as soluções
de sistemas de controlo lineares no controlo. As suas trajetórias são representadas
pelas chamadas séries de Chen. Estuda-se a representação formal
destas séries através da introdução de várias álgebras não associativas e
técnicas específicas de álgebras de Lie livres. Sistemas de coordenadas para
estes sistemas são estudados, nomeadamente, coordenadas de primeiro tipo
e de segundo tipo. Apresenta-se uma demonstração alternativa para as
coordenadas de segundo tipo e obtêm-se expressões explícitas para as coordenadas
de primeiro tipo. Estas últimas estão intimamente ligadas ao
logaritmo da série de Chen que, por sua vez, tem fortes relações com
uma fórmula designada na literatura por “continuous Baker-Campbell-
Hausdorff formula”. São ainda apresentadas aplicações à teoria de funções
simétricas não comutativas. É, por fim, caracterizado o mapa de monodromia
de um campo de vectores não linear e periódico no tempo em relação
a uma truncatura do logaritmo de Chen.
No segundo tópico é estudada a estabilizabilidade de um sistema de quaisquer
dois corpos que rolem um sobre o outro sem deslizar ou torcer.
Constroem-se controlos fechados e dependentes do tempo que tornam a
origem do sistema de dois corpos num sistema localmente assimptoticamente
estável. Vários exemplos e algumas implementações em Maple°c
são discutidos.
No terceiro tópico, em apêndice, constroem-se algoritmos para calcular o
valor de várias funções fundamentais na aritmética digital, sendo possível
a sua implementação em microprocessadores. São também obtidos os seus
domínios de convergência.
No último tópico, também em apêndice, demonstra-se a existência e unicidade
de solução para uma classe de equações integrais não lineares com
atraso. O atraso tem um carácter funcional, mostrando-se ainda a diferenciabilidade
no sentido de Fréchet da solução em relação à função de atraso.<br>In this PhD thesis several subjects are studied regarding the following topics:
formulas for nonlinear control systems on free Lie algebras, stabilizability
of nonlinear control systems, digital arithmetic algorithms, and nonlinear
Fredholm integral equations with delay.
The first and principal topic is mainly related with a problem known as the
continuous Baker-Campbell-Hausdorff exponents. We propose a calculus
to deal with formal nonautonomous ordinary differential equations evolving
on the algebra of formal series defined on an alphabet. We introduce and
connect several (non)associative algebras as Lie, shuffle, zinbiel, pre-zinbiel,
chronological (pre-Lie), pre-chronological, dendriform, D-I, and I-D. Most of
those notions were also introduced into the universal enveloping algebra of
a free Lie algebra. We study Chen series and iterated integrals by relating
them with nonlinear control systems linear in control. At the heart of
all the theory of Chen series resides a zinbiel and shuffle homomorphism
that allows us to construct a purely formal representation of Chen series
on algebras of words. It is also given a pre-zinbiel representation of the
chronological exponential, introduced by A.Agrachev and R.Gamkrelidze
on the context of a tool to deal with nonlinear nonautonomous ordinary
differential equations over a manifold, the so-called chronological calculus.
An extensive description of that calculus is made, collecting some
fragmented results on several publications. It is a fundamental tool of
study along the thesis. We also present an alternative demonstration
of the result of H.Sussmann about coordinates of second kind using
the mentioned tools. This simple and comprehensive proof shows that
coordinates of second kind are exactly the image of elements of the dual
basis of a Hall basis, under the above discussed homomorphism. We obtain
explicit expressions for the logarithm of Chen series and the respective
coordinates of first kind, by defining several operations on a forest of
leaf-labelled trees. It is the same as saying that we have an explicit
formula for the functional coefficients of the Lie brackets on a continuous
Baker-Campbell-Hausdorff-Dynkin formula when a Hall basis is used. We
apply those formulas to relate some noncommutative symmetric functions,
and we also connect the monodromy map of a time-periodic nonlinear
vector field with a truncation of the Chen logarithm.
On the second topic, we study any system of two bodies rolling one
over the other without twisting or slipping. By using the Chen logarithm
expressions, the monodromy map of a flow and Lyapunov functions, we
construct time-variant controls that turn the origin of a control system
linear in control into a locally asymptotically stable equilibrium point.
Stabilizers for control systems whose vector fields generate a nilpotent Lie
algebra with degree of nilpotency · 3 are also given. Some examples are
presented and Maple°c were implemented.
The third topic, on appendix, concerns the construction of efficient
algorithms for Digital Arithmetic, potentially for the implementation in
microprocessors. The algorithms are intended for the computation of
several functions as the division, square root, sines, cosines, exponential,
logarithm, etc. By using redundant number representations and methods
of Lyapunov stability for discrete dynamical systems, we obtain several
algorithms (that can be glued together into an algorithm for parallel execution)
having the same core and selection scheme in each iteration. We also prove
their domains of convergence and discuss possible extensions.
The last topic, also on appendix, studies the set of solutions of a class
of nonlinear Fredholm integral equations with general delay. The delay
is of functional character modelled by a continuous lag function. We
ensure existence and uniqueness of a continuous (positive) solution of such
equation. Moreover, under additional conditions, it is obtained the Fr´echet
differentiability of the solution with respect to the lag function.
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CARAFFA, BERNARD Daniela. "Equations aux dérivées partielles elliptiques du quatrième ordre avec exposants critiques de Sobolev sur les variétés riemanniennes avec et sans bord." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2003. http://tel.archives-ouvertes.fr/tel-00003179.
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L'objet de cette thèse est l'étude, sur les variétés riemanniennes compactes $(V_n,g)$ de dimension $n>4$, de l'équation aux dérivées partielles elliptique de quatrième ordre $$(E)\; \Delta^2u+\nabla [a(x)\nabla u] +h(x)u= f(x)|u|^(N-2)u$$ où $a$, $h$, $f$ sont fonction $C^\infty $, avec $f(x)$ fonction constante ou partout positive et $N=(2n\over((n-4)))$ est l'exposant critique. En utilisant la méthode variationnelle on prouve dans le théorème principal que l'équation $(E)$ admet une solution $C^((5,\alpha))(V)$ $0<\alpha<1$ non nulle si une certaine condition qui dépend de la meilleure constante dans les inclusion de Sobolev ($H_2\subset L_(2n\over(n-4))$) est satisfaite. De plus on montre que si $a$ et $h$ sont des fonctions constantes bien précisées la solution de l'équation est positive et $C^\infty(V)$. Lorsque $n\geq 6$, on donne aussi des applications du théorème principal. Dans la dernière partie de cette thèse sur une variété riemannienne compacte à bord de dimension $n$, $(\overline(W)_n,g )$ nous nous intéressons au problème : $$ (P_N) \; \left\lbrace \begin(array)(c) \Delta^2 v+\nabla [a(x)\nabla u] +h(x) v= f(x)|v |^(N-2)v \; \hbox(sur)\; W \\ \Delta v =\delta \, , \, v = \eta \;\hbox(sur) \;\partial W \end(array)\right.$$ avec $\delta$,$\eta$,$f$ fonctions $C^\infty (\overline (W))$ avec $f(x)$ fonction partout positive et on démontre l'existence d'une solution non triviale pour le problème $(P_N)$.
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"A study of heteroclinic orbits for a class of fourth order ordinary differential equations." Université catholique de Louvain, 2004. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-11292004-111053/.
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CHIEN, HSIU-CHUN, and 簡秀純. "Existence of Anti-periodic Solution for Nonlinear Higher Order Ordinary Differential Equations." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/6nhq7h.
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碩士<br>國立臺北教育大學<br>數學暨資訊教育學系(含數學教育碩士班)<br>96<br>In this paper, we prove several new existence results for a nonlinear anti-periodic nth-order problem using a Leray-Schauder alternative to find the existence of solutions for (BVP).
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Wu, Wen Hsien, and 吳文賢. "On the oscillation properties of some second order nonlinear ordinary differential equations." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/37640683068982389182.
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碩士<br>中原大學<br>應用數學研究所<br>83<br>In the last two decades the problem of finding sufficient
conditions for the oscillation of all solutions of ordinary
differential equations has begun to receive more and more
attention. The aim of this paper is to discuss the oscillatory
behavior of solutions of the nonlinear differential equations:
(a(t)x'(t))'+P(t)f(x'(t))+Q(t)g(x(t),x(q(t)))=r(t) and (r(t)ψ(
y(t))φ(y'(t)))'+P(t)K(t,y(t),y'(t))y'(t) +Q(t)f(y(t))=0 and
the more general equation (r(t)ψ(y(t))φ(y'(t)))'+P(t)K(t,y(t),
y'(t))φ(y'(t)) +Q(t,y(t))=H(t,y(t),φ(y'(t))) A solution is
said to be oscillatory if it has arbitrarily large zeros, and
otherwise it is said to be nonoscillatory. Equation is called
oscillatory if all its solutions are oscillatory. The results
we obtained defend and extend some of those of [2],[3],[4]. We
also extend and improve the result of [1].
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Yu, Chi-Jer, and 余啟哲. "The Bifurcation Analysis of the N-th Order, Nonlinear Ordinary Differential Equations." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/20155518528129413382.
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碩士<br>國立交通大學<br>應用數學研究所<br>82<br>In this thesis, we develped both the theoretic and numerical
tools to investigate the bifurcation dynamics of the general
nonlinear,high-dimensional ODEs. Our numerical code is then
developed and applied to the N-mode truncated, perturbed
nonlinear Schrodinger equation (which is specified later) to do
the pratical computations. The results are completely
consistent with the previous work done by Chuyu Xiong [11],
which is also the main reference in our study.
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SU, GUI-FANG, and 蘇貴芳. "The order of convergence and error estimates for (A, B) methods for ordinary differential equations." Thesis, 1986. http://ndltd.ncl.edu.tw/handle/01862740075271195671.
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Erh-Tsung, Chin, and 秦爾聰. "Solutions of a Class of Nth Order Ordinary and Partial Differential Equations via Fractional Calculus." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/w7dx38.
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碩士<br>中原大學<br>數學研究所<br>86<br>In the vast literature on fractional calculus, one can find many systematicaccounts of its theory and applications in a lot of fields. The method offractional calculus is very simple and useful for obtaining the solutions of certain non-homogeneous linear differential equations. Many papers have been published. After studying these papers, the motive of this thesis arises: Is it possible to deduce a general formula for obtaining the solutions of certain Nth order differential equations with n singular points? Therefore, aboveall, we carry on the idea of "Solution of a class of third order ordinary andpartial differential equations via fractional calculus" and deal with the solutions of another certain third order differential equations . Consequently, all the solutions of certin third order differential equations (ordinary or partial) with three singular points are discussed. Finally, we extend this concept to certain Nth order differential equations with n singular points . Actually, this thesis is a synthesis of two published papers. Some results given by Nishimoto, Al-Saqabi, Kalla, and Tu can be included as particular cases of our theorems.
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Chuang, Hsiao-Chin, and 莊筱秦. "Existence of solutions for high order ordinary differential equations with some periodic-type boundary condition." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/6c9pxy.
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碩士<br>國立臺北教育大學<br>數學暨資訊教育學系(含數學教育碩士班)<br>98<br>We consider the following high order periodic-type boundary value problem and satisfies the so-called Nagumo’s condition. In this article, we will use a general upper and lower solution method to establish an existence theorem for solutions of .
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You, L. H., Hassan Ugail, B. P. Tang, X. Jin, X. Y. You, and J. J. Zhang. "Blending using ODE swept surfaces with shape control and C1 continuity." 2014. http://hdl.handle.net/10454/8167.
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No<br>Surface blending with tangential continuity is most widely applied in computer-aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: (1) exact satisfaction of C1C1 continuous blending boundary constraints, (2) effective shape control of blending surfaces, (3) high computing efficiency due to explicit mathematical representation of blending surfaces, and (4) ability to blend multiple (more than two) primary surfaces.
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"On conformally invariant fourth order elliptic equations." 1999. http://library.cuhk.edu.hk/record=b5889927.
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by Chin Pang Cheung.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.<br>Includes bibliographical references (leaves 38-39).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Main Results and Introduction --- p.4<br>Chapter 1.1 --- Preliminaries --- p.5<br>Chapter 2 --- The Linearized Operator in the Weighted Sobolev Spaces --- p.8<br>Chapter 2.1 --- Weighted Sobolev Space and Some Useful Properties --- p.8<br>Chapter 2.2 --- The Linearized Operator --- p.10<br>Chapter 3 --- Reduction to Finite Dimensions --- p.19<br>Chapter 4 --- Reduced Problem --- p.27<br>Chapter 4.1 --- Proof of Theorem 1.1 --- p.27<br>Chapter 4.2 --- Asymptotic Behavior of uE --- p.34<br>Bibliography
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Yan, Jing-Kai, and 顏靖凱. "On the homoclinic solutions of fourth order differential equations." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/10795576420728964663.
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碩士<br>國立高雄大學<br>應用數學系碩士班<br>103<br>In this paper,we consider a class of nonperiodic fourth-order
differential equations with a perturbation:
u^(4)+wu''+a(x)u-f(x,u)=0,x∈R (1)
where w≤0 is a constant, f∈C(R×R,R) and a∈C(R,R) The above equation (1)
has been put forward as mathematical model for the study of pattern
formation in physics and mechanics. The aim of this paper is to
consider the existence of homoclinic solutions for the nonperiodic
fourth order equations with a perturbation. We shall establish a new
compactness lemma which is different from that in [12] and
obtain the result of the existence of homoclinic solutions.
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Yang, Mei-Chen, and 楊美真. "On the Existence of Positive Solutions for Higher Order Ordinary Differential Equation." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/38910321751065601271.
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碩士<br>淡江大學<br>數學系<br>83<br>In this paper we are concerned with the existence of positive
solutions of boundary value problems of the form #1 ,in the
case that f is either superlinear or sublinear.The methods
involve application of fixed point theorem for operators on a
cone.
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Mohanty, Ranjan Kumar. "Fourth order finite difference method for certain mildly nonlinear partial differential equations." Thesis, 1989. http://localhost:8080/xmlui/handle/12345678/4736.
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Medri, Ivan Vladimir. "Soluciones positivas para problemas elípticos sublineales y singulares." Doctoral thesis, 2018. http://hdl.handle.net/11086/6148.
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Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2018.<br>En esta tesis se estudiaron tres problemas relacionados a ecuaciones de reacción difusión elípticas sublineales y singulares cuando el término de reacción cambia de signo. En primer lugar se trató la existencia y no existencia de soluciones estrictamente positivas para problemas sublineales asociados a un operador elíptico lineal de segundo orden en el caso unidimensional. Además, se consideró la existencia y unicidad de soluciones no negativas en el caso multidimensional. En segundo lugar, también en una dimensión, se estudiaron problemas sublineales asociados a operadores que involucran al p-Laplaciano. Finalmente, se estudió la existencia y no existencia de soluciones positivas asociadas al p-Laplaciano cuando el término de reacción es singular. En este último caso se obtuvieron resultados cuantitativos en dimensión uno y cualitativos en dimensiones mayores.<br>Fil: Medri, Ivan Vladimir. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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Exnerová, Vendula. "Bifurkace obyčejných diferenciálních rovnic z bodů Fučíkova spektra." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-300427.
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Title: Bifurcation of Ordinary Differential Equations from Points of Fučík Spectrum Author: Vendula Exnerová Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Jana Stará, CSc., Department of Mathematical Analysis MFF UK, Prague Abstract: The main subject of the thesis is the Fučík spectrum of a system of two differential equations of the second order with mixed boundary conditions. In the first part of the thesis there are described Fučík spectra of problems of a differential equation with Dirichlet, mixed and Neumann boundary conditions. The other part deals with systems of two differential equations. It attends to basic properties of systems and their nontrivial solutions, to a possibility of a reduction of number of parameters and to a dependance of a problem with mixed boundary condition on one with Dirichlet boundary conditions. The thesis takes up the results of E. Massa and B. Ruff about the Dirichlet problem and improves some of their proofs. In the end the Fučík spectrum of a problem with mixed boundary conditions is described as the union of countably many continuously differentiable surfaces and there is proven that this spectrum is closed.
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Moletsane, Boitumelo. "Spectral properties of a fourth order differential equation with eigenvalue dependent boundary conditions." Thesis, 2012. http://hdl.handle.net/10539/11340.
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Behera, Kshyanaprabha. "Numerical solution of uncertain second order ordinary differential equation using interval finite difference method." Thesis, 2012. http://ethesis.nitrkl.ac.in/3277/1/Numerical_Solution_of_Uncertain_Second_Order_Ordinary_Differential_Equation_Using_Interval_Finite_Difference_Method.pdf.
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It is well known that differential equations are in general the backbone of physical systems. The physical systems are modelled usually either by ordinary differential or partial differential equations. Various exact and numerical methods are available to solve different ordinary and partial differential equations. But in actual practice the variables and coefficients in the differential equations are not crisp. As those, are obtained by some experiment or experience. As such the coefficients and the variables may be used in interval or in fuzzy sense. So, we need to solve ordinary and partial differential equations accordingly, that is interval ordinary and interval partial differential equations are to be solved. In the present analysis our target is to use interval computation in the numerical solution of some ordinary differential equations of second order by using interval finite difference method with uncertain analysis.
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Saum, Michael Authur. "Adaptive discontinuous Galerkin finite element methods for second and fourth order elliptic partial differential equations." 2006. http://etd.utk.edu/2006/SaumMichael.pdf.
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Thesis (Ph. D.) -- University of Tennessee, Knoxville, 2006.<br>Title from title page screen (viewed on Sept. 15, 2006). Thesis advisor: Ohannes Karakashian. Vita. Includes bibliographical references.
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Tsai, Chia-Hsing, and 蔡嘉星. "Solve Vector Potential Formulation of Navier-Stokes Equations: Using Fourth-Order-Accuracy Localized Differential Quadrature Method." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/13040757048590468141.
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博士<br>國立臺灣大學<br>土木工程學研究所<br>99<br>To simulate three-dimensional flow problems in this thesis, the vector potential formulations of three-dimensional incompressible Navier-Stokes are chosen to govern the motion of fluid flow. The vector potential formulation belongs to one of the pressure-free algorithms which are obtained by taking curl to the momentum equations. By replacing the vorticity with Laplacian vector potential to the vorticity transport equations, the Navier-Stokes equations are transformed to fourth-order partial differential equations (PDEs) with one variable---vector potential. Comparing with other pressure-free algorithms, vector potential formulations are simpler and more accurate, and, moreover, the computation is more efficient. To the boundary conditions of vector potential, except the presented defined boundary conditions for confined flow, we further improved the algorithm to through-flow problem by introducing the concept of Stokes'' theorem. To author''s best knowledge, this improvement is groundbreaking. To accurately approximate these fourth-order governing equations, fourth-order-accuracy localized differential quadrature (LDQ) methods are employed. Through adopting the non-uniform mesh grids, the solutions can be obtained efficiently. To examine the ability of the proposed scheme to fourth-order governing equations, two benchmark problems are considered, including two-dimensional cavity flow problems and backward-facing step flow problems. The results show the accuracy and feasibility of the proposed scheme. By the successful implementation of the present scheme to two-dimensional flow problems, the proposed scheme is further employed to solve three-dimensional benchmark problems, including three-dimensional driven cavity flow problems and backward-facing step flow problems. The good performance not only demonstrates that the proposed scheme is able to be employed to solve the vector potential formulation, but also validates the correctness of the presented formulation. Furthermore, we specifically visualized the contour of vector potential by numerical simulation. The comparison between vector potential and stream functions show the difference of these two algorithms. Conclusively, the vector potential formulations of Navier-Stokes equations are successfully used to simulate the three-dimensional fluid motion, especially the fluid flow problems with through-flow. Through the application of the fourth-order-accuracy of localized differential quadrature method, the solutions can be accurately obtained, and the vector potential can be specifically visualized. From the previous literatures, no literature has ever presented the similar idea of this research. It is convinced that the groundbreaking findings in this thesis can provide a feasible way to simulate three-dimensional fluid motion.
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Gopalsamy, S. "Mixed/equilibrium/hybrid finite element methods for fourth order elliptic partial differential equations with variable coefficients." Thesis, 1987. http://localhost:8080/xmlui/handle/12345678/4724.
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Arnal, A., J. Monterde, and Hassan Ugail. "Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation." 2011. http://hdl.handle.net/10454/9031.
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No<br>We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discuss a series of examples which utilize the explicit solutions to generate smooth surfaces that interpolate a given boundary configuration. We compare the speed of our explicit solution scheme with the solution arising from directly solving the associated linear system.
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Held, Joachim. "Ein Gebietszerlegungsverfahren für parabolische Probleme im Zusammenhang mit Finite-Volumen-Diskretisierung." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B39E-E.
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