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Relevant bibliographies by topics / Caratheodory solutions of differential equations

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Academic literature on the topic 'Caratheodory solutions of differential equations'

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Published: 24 April 2022

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Journal articles on the topic "Caratheodory solutions of differential equations"

1

Alsaedi, Ahmed, Dumitru Baleanu, Sina Etemad, and Shahram Rezapour. "On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative." Journal of Function Spaces 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/4626940.

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The existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact- and convex-valuedL1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.

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2

Liu, Yuji. "MULTIPLE POSITIVE SOLUTIONS OF BVPS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-CARATHEODORY NONLINEARITIES." Mathematical Modelling and Analysis 19, no. 3 (2014): 395–416. http://dx.doi.org/10.3846/13926292.2014.925984.

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In this article, the existence of multiple positive solutions of boundary-value problems for nonlinear singular fractional order elastic beam equations is established. Here f depends on x, x′ and x″, f may be singular at t = 0 and t = 1 and f is non-Caratheodory function. The analysis relies on the well known Schauder fixed point theorem and the five functional fixed point theorems in the cones.

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Yeh, Nai-Sher. "On Solvability Theorems of Second-Order Ordinary Differential Equations with Delay." Abstract and Applied Analysis 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/5321314.

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For eachx0∈[0,2π)andk∈N, we obtain some existence theorems of periodic solutions to the two-point boundary value problemu′′(x)+k2u(x-x0)+g(x,u(x-x0))=h(x)in(0,2π)withu(0)-u(2π)=u′(0)-u′(2π)=0wheng:(0,2π)×R→Ris a Caratheodory function which grows linearly inuasu→∞, andh∈L1(0,2π)may satisfy a generalized Landesman-Lazer condition(1+sign(β))∫02πh(x)v(x)dx<∫v(x)>0gβ+(x)vx1-βdx+∫v(x)<0gβ-(x)vx1-βdxfor allv∈N(L)\{0}. HereN(L)denotes the subspace ofL1(0,2π)spanned bysin⁡kxandcos⁡kx,-1<β≤0,gβ+(x)=lim infu→∞(gx,uu/u1-β), andgβ-(x)=lim infu→-∞(gx,uu/u1-β).

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Mukhigulashvili, Sulkhan, and Mariam Manjikashvili. "DIRICHLET BVP FOR THE SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS AT RESONANCE." Mathematical Modelling and Analysis 24, no. 4 (2019): 585–97. http://dx.doi.org/10.3846/mma.2019.035.

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Landesman-Lazer’s type efficient sufficient conditions are established forthe solvability of the Dirichlet problem u′′(t) = p(t)u(t) + f(t, u(t)) + h(t),for a ≤ t ≤ b, u(a) = 0, u(b) = 0, where h, p ϵ L([a, b];R) and f is the L([a, b];R) Caratheodory function, in the casewhere the linear problem u′′(t) = p(t)u(t), u(a) = 0,u(b) = 0 has nontrivial solutions. The results obtained in the paper are optimal in the sense that if f ≡ 0,i.e., when nonlinear equation turns to the linear equation, from our results follows the first partof Fredholm’s theorem.

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Mesmouli, Mouataz Billah, Abdelouaheb Ardjouni, and Ahcene Djoudi. "Study of periodic and nonnegative periodic solutions of nonlinear neutral functional differential equations via fixed points." Acta Universitatis Sapientiae, Mathematica 8, no. 2 (2016): 255–70. http://dx.doi.org/10.1515/ausm-2016-0017.

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Abstract In this paper, we study the existence of periodic and non-negative periodic solutions of the nonlinear neutral differential equation $${{\rm{d}} \over {{\rm{dt}}}}{\rm{x}}({\rm{t}}) = - {\rm{a}}\;({\rm{t}})\;{\rm{h}}\;({\rm{x}}\;({\rm{t}})) + {{\rm{d}} \over {{\rm{dt}}}}{\rm{Q}}\;({\rm{t}},\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))) + {\rm{G}}\;({\rm{t}},\;{\rm{x}}({\rm{t}}),\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))).$$ We invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for applying the modificatition of Kra

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6

Lipcsey, Z., J. A. Ugboh, I. M. Esuabana, and I. O. Isaac. "Existence Theorem for Impulsive Differential Equations with Measurable Right Side for Handling Delay Problems." Journal of Mathematics 2020 (June 26, 2020): 1–17. http://dx.doi.org/10.1155/2020/7089313.

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Due to noncontinuous solution, impulsive differential equations with delay may have a measurable right side and not a continuous one. In order to support handling impulsive differential equations with delay like in other chapters of differential equations, we formulated and proved existence and uniqueness theorems for impulsive differential equations with measurable right sides following Caratheodory’s techniques. The new setup had an impact on the formulation of initial value problems (IVP), the continuation of solutions, and the structure of the system of trajectories. (a) We have two impuls

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Zhukovskaia, Tatiana V., Olga V. Filippova, and Andrey I. Shindiapin. "On the extension of Chaplygin’s theorem to the differential equations of neutral type." Tambov University Reports. Series: Natural and Technical Sciences, no. 127 (2019): 272–80. http://dx.doi.org/10.20310/2686-9667-2019-24-127-272-280.

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We consider functional-differential equation x ̇((g(t) )= f(t; x(h(t) ) ),t ∈ [0; 1], where function f satisfies the Caratheodory conditions, but not necessarily guarantee the boundedness of the respective superposition operator from the space of the essentially bounded functions into the space of integrable functions. As a result, we cannot apply the standard analysis methods (in particular the fixed point theorems) to the integral equivalent of the respective Cauchy problem. Instead, to study the solvability of such integral equation we use the approach based not on the fixed point theorems

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Magomed-Kasumov, M. G. "Теоремы существования и единственности для дифференциального уравнения с разрывной правой частью". Владикавказский математический журнал, № 1 (29 березня 2022): 54–64. http://dx.doi.org/10.46698/p7919-5616-0187-g.

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We consider new conditions for existence and uniqueness of a Caratheodory solution for an initial value problem with a discontinuous right-hand side. The method used here is based on:1) the representation of the solution as a Fourier series in a system of functions orthogonal in Sobolev sense and generated by a classical orthogonal system;2) the use of a specially constructed operator $A$ acting in $l_2$, the fixed point of which are the coefficients of the Fourier series of the solution.Under conditions given here the operator $A$ is contractive. This property can be employed to construct rob

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Potzsche, C., and M. Rasmussen. "Computation of integral manifolds for Caratheodory differential equations." IMA Journal of Numerical Analysis 30, no. 2 (2008): 401–30. http://dx.doi.org/10.1093/imanum/drn059.

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10

Noroozi, Hossein, Alireza Ansari, and Mohammad Shafi Dahaghin. "Existence Results for the Distributed Order Fractional Hybrid Differential Equations." Abstract and Applied Analysis 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/163648.

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We introduce the distributed order fractional hybrid differential equations (DOFHDEs) involving the Riemann-Liouville differential operator of order0<q<1with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved via a fixed point theorem in the Banach algebras under the mixed Lipschitz and Caratheodory conditions.

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Dissertations / Theses on the topic "Caratheodory solutions of differential equations"

1

Tarkhanov, Nikolai. "Unitary solutions of partial differential equations." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2985/.

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2

Head, Gerald. "Uniqueness of Solutions of Differential Equations." TopSCHOLAR®, 1995. http://digitalcommons.wku.edu/theses/913.

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Uniqueness of solutions for ordinary differential equations is studied. The classical theorems which guarantee uniqueness are surveyed, including discussion and examples. Other results concerning uniqueness are considered in the final chapter, including the relationship between convergence of successive approximations and uniqueness, non-uniqueness and continuous dependence on initial conditions.

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Mohrenschildt, Martin von. "Symbolic solutions of discontinuous differential equations /." [S.l.] : [s.n.], 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10768.

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Wu, Chengfa, and 吳成發. "Meromorphic solutions of complex differential equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206466.

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The objective of this thesis is to study meromorphic solutions of complex algebraic ordinary differential equations (ODEs). The thesis consists of two main themes. One of them is to find explicitly all meromorphic solutions of certain class of complex algebraic ODEs. Since constructing explicit solutions of complex ODEs in general is very difficult, the other theme (motivated by the classical conjecture proposed by Hayman in 1996) is to establish estimations on the growth of meromorphic solutions in terms of Nevanlinna characteristic function. The tools from complex analysis that will be us

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Lloyd, David J. B. "Localised solutions of partial differential equations." Thesis, University of Bristol, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434765.

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Lagrange, John. "Power Series Solutions to Ordinary Differential Equations." TopSCHOLAR®, 2001. http://digitalcommons.wku.edu/theses/672.

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In this thesis, the reader will be made aware of methods for finding power series solutions to ordinary differential equations. In the case that a solution to a differential equation may not be expressed in terms of elementary functions, it is practical to obtain a solution in the form of an infinite series, since many differential equations which yield such a solution model an actual physical situation. In this thesis, we introduce conditions that guarantee existence and uniqueness of analytic solutions, both in the linear and nonlinear case. Several methods for obtaining analytic solutions a

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Bratsos, A. G. "Numerical solutions of nonlinear partial differential equations." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332806.

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8

Lumb, Patricia M. "Delay differential equations : detection of small solutions." Thesis, University of Chester, 2004. http://hdl.handle.net/10034/68595.

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This thesis concerns the development of a method for the detection of small solutions to delay differential equations. The detection of small solutions is important because their presence has significant influence on the analytical prop¬erties of an equation. However, to date, analytical methods are of only limited practical use. Therefore this thesis focuses on the development of a reliable new method, based on finite order approximations of the underlying infinite dimen¬sional problem, which can detect small solutions. Decisions (concerning the existence, or otherwise, of small solutions) ba

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9

Hemmi, Mohamed Ali Carleton University Dissertation Mathematics and statistics. "Series solutions of nonlinear ordinary differential equations." Ottawa, 1994.

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10

Dowie, Ellen. "Rational solutions of nonlinear partial differential equations." Thesis, University of Kent, 2018. https://kar.kent.ac.uk/66565/.

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The work in this thesis considers rational solutions of nonlinear partial differential equations formed from polynomials. The main work will be on the Boussinesq equation and the Kadomtsev-Petviashvili-I (KP-I) equation, the nonlinear Schroedinger equation will also be included for completeness. Rational solutions of the Boussinesq equation model rogue wave behaviour. These solutions are shown to be highly structured which, it is hypothesised, is due to the inherent structure and form of integrable differential equations. Rogue wave solutions have been observed in equations such as the nonline

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Books on the topic "Caratheodory solutions of differential equations"

1

Solutions of partial differential equations. Tab Professional and Reference Books, 1986.

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1944-, Nørsett S. P., and Wanner Gerhard, eds. Solving ordinary differential equations. Springer-Verlag, 1987.

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Hairer, E. Solving ordinary differential equations. 2nd ed. Springer, 1996.

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1944-, Nørsett S. P., and Wanner Gerhard, eds. Solving ordinary differential equations. 2nd ed. Springer-Verlag, 1993.

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Hairer, E. Solving ordinary differential equations. Springer-Verlag, 1991.

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Mason, J. C. BASIC differential equations. Boston, 1987.

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Mason, J. C. BASIC differential equations. Butterworths, 1987.

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Snider, Arthur David. Partial differential equations: Sources and solutions. Dover Publications, 2006.

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9

Generalized solutions of functional differential equations. World Scientific, 1993.

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10

YI, Zhang. Periodic solutions of neutral differential equations. University ofSheffield, Dept. of Control Engineering, 1990.

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Book chapters on the topic "Caratheodory solutions of differential equations"

1

Filippov, V. V. "Peano, Caratheodory and Davy Conditions." In Basic Topological Structures of Ordinary Differential Equations. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-0841-8_8.

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Kevorkian, J. "Perturbation Solutions." In Partial Differential Equations. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-9022-0_8.

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Jost, Jürgen. "Strong Solutions." In Partial Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4809-9_12.

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Struthers, Allan, and Merle Potter. "Series Solutions for Differential Equations." In Differential Equations. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20506-5_7.

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Dey, Anindya. "Series Solutions of Linear Differential Equations." In Differential Equations. CRC Press, 2021. http://dx.doi.org/10.1201/9781003205982-8.

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Fässler, Albert. "Solutions." In Fast Track to Differential Equations. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23291-7_6.

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Fässler, Albert. "Solutions." In Fast Track to Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83450-0_7.

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Fässler, Albert. "Solutions." In Fast Track to Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83450-0_7.

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Napolitano, Jim. "Differential Equations: Analytic Solutions." In A Mathematica Primer for Physicists. CRC Press, 2018. http://dx.doi.org/10.1201/b21981-4.

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Napolitano, Jim. "Differential Equations: Numerical Solutions." In A Mathematica Primer for Physicists. CRC Press, 2018. http://dx.doi.org/10.1201/b21981-5.

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Conference papers on the topic "Caratheodory solutions of differential equations"

1

Żołądek, Henryk. "Polynomial Riccati equations with algebraic solutions." In Differential Galois Theory. Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc58-0-17.

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Dorodnitsyn, Vladimir A., Roman Kozlov, Sergey V. Meleshko, and Pavel Winternitz. "Invariant solutions of delay differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044161.

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Akgül, A., and M. Giyas Sakar. "On solutions of fractional differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044175.

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Morimoto, M., and T. Kawai. "Structure of Solutions of Differential Equations." In Katata/Kyoto, 1995. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814532570.

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MA, YUJIE, and XIAO-SHAN GAO. "POLYNOMIAL SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS." In Proceedings of the Fifth Asian Symposium (ASCM 2001). WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812799661_0010.

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Mortari, Daniele, Hunter R. Johnston, and Lidia I. Smith. "Least-Squares Solutions of Nonlinear Differential Equations." In 2018 Space Flight Mechanics Meeting. American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-0959.

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Anashkin, Oleg. "Bifurcations of solutions of impulsive differential equations." In 2018 14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference) (STAB). IEEE, 2018. http://dx.doi.org/10.1109/stab.2018.8408341.

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FAGNOLA, FRANCO. "REGULAR SOLUTIONS OF QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS." In Quantum Stochastics and Information - Statistics, Filtering and Control. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832962_0002.

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Vasilyev, Vladimir. "On discrete solutions for pseudo-differential equations." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114031.

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Abramov, Sergei A., and Marko Petkovšek. "D'Alembertian solutions of linear differential and difference equations." In the international symposium. ACM Press, 1994. http://dx.doi.org/10.1145/190347.190412.

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Reports on the topic "Caratheodory solutions of differential equations"

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Gilsinn, David E. Approximating periodic solutions of autonomous delay differential equations. National Institute of Standards and Technology, 2006. http://dx.doi.org/10.6028/nist.ir.7375.

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Zweig, G. Wavelet transforms as solutions of partial differential equations. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/534535.

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Pulov, Vladimir. Construction of Group-Invariant Solutions of Partial Differential Equations. GIQ, 2012. http://dx.doi.org/10.7546/giq-13-2012-258-264.

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Herzog, K. J., M. D. Morris, and T. J. Mitchell. Bayesian approximation of solutions to linear ordinary differential equations. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6242347.

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Bao, Gang, and William W. Symes. A Trace Theorem for Solutions of Linear Partial Differential Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada455263.

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A. R. Esfandyari, A. R. Esfandyari. Solitary Solutions of Coupled KdV and Hirota–Satsuma Differential Equations. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-196-208.

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Saltzman, J. Patched based methods for adaptive mesh refinement solutions of partial differential equations. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/584924.

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Webster, Clayton G., Guannan Zhang, and Max D. Gunzburger. An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1081925.

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Dresner, L. Asymptotic behavior of solutions of diffusion-like partial differential equations invariant to a family of affine groups. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6697591.

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Cornea, Emil, Ralph Howard, and Per-Gunnar Martinsson. Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada640692.

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