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Dissertations / Theses on the topic 'Liouville systems'

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Published: 14 March 2023

Last updated: 31 July 2025

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1

Battaglia, Luca. "Variational aspects of singular Liouville systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4857.

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I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.

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2

Jevnikar, Aleks. "Variational aspects of Liouville equations and systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4847.

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3

Holtz, Susan Lady. "Liouville resolvent methods applied to highly correlated systems." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49795.

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4

Altundag, Huseyin. "Inverse Sturm-liouville Systems Over The Whole Real Line." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612693/index.pdf.

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In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization techniques to overcome the ill-posedness difficulty. Moreover, since the problem is nonli

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5

Aldrovandi, Ettore. "Liouville Field Theory, Drinfel'd-Sokolov Linear Systems and Riemann Surfaces." Doctoral thesis, SISSA, 1992. http://hdl.handle.net/20.500.11767/4292.

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6

Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.

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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schr&ouml<br>dinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of s

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7

Schirmer, Sonja G. "Theory of control of quantum systems /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.

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Thesis (Ph. D.)--University of Oregon, 2000.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.

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8

Medeira, Cléber de. "Resolubilidade global para uma classe de sistemas involutivos." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-15062012-162546/.

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Estudamos a resolubilidade global de uma classe de sistemas involutivos com n campos vetoriais suaves definidos no toro de dimensão n + 1. Obtemos uma caracterização completa para o caso desacoplado desta classe em termos de formas de Liouville e da conexidade de todos os subníveis e superníveis, no espaço de recobrimento minimal, de uma primitiva global da 1-forma associada ao sistema. Além disso, apresentamos uma situação especial na qual o sistema não é globalmente resolúvel e usamos isso para obter alguns resultados em um caso com acoplamento mais forte<br>We study the global solvability o

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9

McAnally, Morgan Ashley. "Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7423.

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We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries,

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10

PEZZOLO, FABIO. "On some multilinear type integral systems." Doctoral thesis, Università degli Studi di Trieste, 2022. http://hdl.handle.net/11368/3015404.

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In this thesis we prove some Liouville theorems for systems of integral equations related to Beckner and Stein-Weiss inequalities on R^N. We consider both variational and non-variational solutions. In order to study the first type of solutions we applied Rellich type identities.<br>In this thesis we prove some Liouville theorems for systems of integral equations related to Beckner and Stein-Weiss inequalities on R^N. We consider both variational and non-variational solutions. In order to study the first type of solutions we applied Rellich type identities.

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11

Liard, Thibault. "Observation et contrôle de quelques systèmes conservatifs." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066364/document.

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Dans cette thèse, nous nous intéressons à la contrôlabilité interne et à son coût pour une ou plusieurs équations aux dérivées partielles conservatives. ?Dans la première partie, nous introduisons et détaillons deux méthodes permettant d'estimer le coût du contrôle (et par dualité, de la constante d'observabilité) de l'équation des ondes avec potentiel $l^{\infty}$ en dimension un d'espace. La première utilise la propagation des ondes le long des caractéristiques en s'appuyant sur le rôle symétrique de la variable de temps et d'espace. La deuxième méthode repose sur la décomposition spectrale

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12

Garrione, Maurizio. "Existence and multiplicity of solutions to boundary value problems associated with nonlinear first order planar systems." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4930.

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The monograph is devoted to the study of nonlinear first order systems in the plane where the principal term is the gradient of a positive and positively 2-homogeneous Hamiltonian (or the convex combination of two of such gradients). After some preliminaries about positively 2-homogeneous autonomous systems, some results of existence and multiplicity of T-periodic solutions are presented in case of bounded or sublinear nonlinear perturbations. Our attention is mainly focused on the occurrence of resonance phenomena, and the corresponding results rely essentially on conditions of Landesman-Laz

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13

Granados, Castro Carlos Mario. "Application of Generalized Sturmian Basis Functions to Molecular Systems." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0041/document.

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Dans cette thèse nous implémentons une approche Sturmienne, qui se sert de fonctions Sturmiennes généralisées (GSFs, en anglais), pour étudier l'ionisation de molécules par collisions de photons ou d'électrons. Comme l'Hamiltonian de la cible est non central, la description de l'ionisation des molécules n'est pas simple. En plus, puisque l'orientation spatiale de la molécule n'est généralement pas déterminée lors des expériences, une question importante à considérer est l'orientation aléatoire de la cible. Dans la littérature, des nombreuses méthodes théoriques ont été proposées pour traiter l

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14

Yang, Qianqian. "Novel analytical and numerical methods for solving fractional dynamical systems." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/35750/1/Qianqian_Yang_Thesis.pdf.

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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional deri

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15

Wahrheit, Markus. "Eigenwertprobleme und Oszillation linearer Hamiltonscher Systeme." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-56228.

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16

Ugur, Omur. "Boundary Value Problems For Higher Order Linear Impulsive Differential Equations." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/686691/index.pdf.

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_I The theory of impulsive di&reg<br>erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di&reg<br>erential equations. In this work, higher order linear impulsive equations at &macr<br>xed moments of impulses together with certain boundary conditions are investigated by making use of a Green&#039<br>s formula, constructed for p

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17

Tentler, Markus. "Rekursionsformeln zur Berechnung der charakteristischen Polynome von symmetrischen Bandmatrizen." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-63854.

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18

Ouaili, Lydia. "Contrôlabilité de quelques systèmes paraboliques." Thesis, Aix-Marseille, 2020. http://theses.univ-amu.fr.lama.univ-amu.fr/200604_OUAILI_351nl894f5gh253lyuyt716uvgkl9_TH.

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Dans cette thèse, on s’intéresse à la contrôlabilité d’équations paraboliques et à son coût. On étudie dans un premier temps, la contrôlabilité à zéro d’un système de deux équations paraboliques couplés en dimension 1 d’espace, pour lesquelles l’opérateur spacial est de type Sturm-Liouville, avec des conditions au bord de type Dirichlet et un contrôle distribué. Par la méthode des moments on montre l’existence d’un temps minimal de contrôlabilité à zéro sous des conditions géométrique sur le couplage des deux équations. Dans un autre travail, rédigé en collaboration avec González-Burgos, on s’

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19

Kárský, Vilém. "Modelování LTI SISO systémů zlomkového řádu s využitím zobecněných Laguerrových funkcí." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-316278.

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This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.

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20

Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150/document.

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Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet d

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21

Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Electronic Thesis or Diss., Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150.

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Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet d

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22

Wang, Chao. "Analyse de quelques problèmes elliptiques et paraboliques semi-linéaires." Phd thesis, Université de Cergy Pontoise, 2012. http://tel.archives-ouvertes.fr/tel-00809045.

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Cette thèse est divisée en deux parties. Dans la première partie, on considère le système de réaction-diffusion-advection (Pε), qui est un modèle d'haptotaxie, mécanisme lié à la dissémination de tumeurs cancéreuses. Le résultat principal concerne la convergence de la solution du systeme (Pε) vers la solution d'un problème à frontière libre (P0) qui est bien défini. Dans la seconde partie, on considère une classe générale d'équations elliptiques du type Hénon:−∆u = |x|^{α} f(u) dans Ω ⊂ R^N avec α > -2. On examine deux cas classiques : f(u) = e^u, |u|^{p−1} u et deux autres cas : f(u) = u^{p}_

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23

SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variationa

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24

Fino, Ahmad. "Contributions aux problèmes d'évolution." Phd thesis, Université de La Rochelle, 2010. http://tel.archives-ouvertes.fr/tel-00437141.

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Dans cette thèse, nous nous intéressons à l'étude de trois équations aux dérivées partielles et d'évolution non-locales en espace et en temps. Les solutions de ces trois solutions peuvent exploser en temps fini. Dans une première partie de cette thèse, nous considérons l'équation de la chaleur nonlinéaire avec une puissance fractionnaire du laplacien, et obtenons notamment que, dans le cas d'exposant sur-critique, le comportement asymptotique de la solution lorsque $t\rightarrow+\infty$ est déterminé par le terme de diffusion anormale. D'autre part, dans le cas d'exposant sous-critique, l'effe

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25

"Generalized Sturm-Liouville theory for dissipative systems." 2004. http://library.cuhk.edu.hk/record=b5892026.

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Lau Ching Yan Ada = 耗散系統中的廣義Sturm-Liouville理論 / 劉正欣.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (leaves 156-157).<br>Text in English; abstracts in English and Chinese.<br>Lau Ching Yan Ada = Hao san xi tong zhong de guang yi Sturm-Liouville li lun / Liu Zhengxin.<br>Abstract --- p.i<br>Acknowledgement --- p.iii<br>Chapter 1 --- Introduction --- p.1<br>Chapter 1.1 --- Vibrational motion in physics --- p.1<br>Chapter 1.2 --- Normal modes of vibration --- p.2<br>Chapter 1.3 --- Boundary conditions --- p.4<br>Chapter 1.4 --- The wave eq

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26

Tiegel, Alexander Clemens. "Finite-temperature dynamics of low-dimensional quantum systems with DMRG methods." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0028-8801-A.

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27

Huang, Yu Ling, and 黃玉玲. "Eigenvalue ratios for the regular Sturm-Liouville system." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/91503865261560745447.

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碩士<br>國立中山大學<br>應用數學研究所<br>82<br>We consider the regular Sturm-Liouville equation on [0,1] (p(x) y')'+(.lambda. w(x)-q(x))y=0 together with separated boundary conditions. In 1993, Ashbaugh and Benguria [2] gave various optimal bounds of eigenvalue ratios for the Sturm- Liouville system with Dirichlet boundary conditions. when q .gdsim. 0. For the general regular Sturm-Liouville system, we prove the various estimates of eigenvalue ratios under the same assumption. For the Neumann boundary co

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28

Wu, Zhi-Jie, and 吳智傑. "Gradient Estimates for System of Semi-linear Equations and Liouville Theorem." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/00443767841521881320.

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碩士<br>國立臺灣大學<br>數學研究所<br>90<br>We generalize the results for a scalar equation by Modica to the case of a system of equations. It is shown that if a bounded entire solution U(x) of a system of semi-linear equations satisfies the gradient bound |\nabla U|^{2}\leq 2F(U) for all x\in \Bbb R^{n}, then the Liouville theorem holds. Also we show that the inequality above holds if $F(U)$ satisfies some suitable assumptions.

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29

Νομικός, Δημήτριος. "Διαφορική θεωρία Galois και μη-ολοκληρωσιμότητα του ανισοτροπικού προβλήματος Stormer και του ισοσκελούς προβλήματος τριών σωμάτων". Thesis, 2010. http://nemertes.lis.upatras.gr/jspui/handle/10889/3876.

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Στην παρούσα διατριβή μελετήσαμε την ολοκληρωσιμότητα του ανισοτροπικού προβλήματος Størmer (ASP) και του ισοσκελούς προβλημάτος τριών σωμάτων (IP), με εφαρμογή της θεωρίας Morales-Ramis-Simó. Τα αποτελέσματα της μελέτης δημοσιεύθηκαν στο περιοδικό Physica D: Nonlinear Phenomena. Ένα σύστημα Hamilton SH, Ν βαθμών ελευθερίας, είναι ολοκληρώσιμο (κατά Liouville) όταν επιδέχεται Ν συναρτησιακώς ανεξάρτητα και σε ενέλιξη πρώτα ολοκληρώματα. Οι J.J. Morales-Ruiz, J.P. Ramis και C. Simó απέδειξαν ότι αν ένα SH είναι ολοκληρώσιμο, τότε η ταυτοτική συνιστώσα G0k της διαφορικής ομάδας Galois των ε

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