Heteroclinic Solutions For A Class Of Fourth Order Ordinary Differential Equations
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A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations
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Author : Denis Bonheure
language : en
Publisher: Presses univ. de Louvain
Release Date : 2004
A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations written by Denis Bonheure and has been published by Presses univ. de Louvain this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.
Heteroclinic Solutions For A Class Of Fourth Order Ordinary Differential Equations
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Author : Denis Bonheure
language : en
Publisher:
Release Date : 2006
Heteroclinic Solutions For A Class Of Fourth Order Ordinary Differential Equations written by Denis Bonheure and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations categories.
Handbook Of Differential Equations Ordinary Differential Equations
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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2006-08-21
Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Mathematics categories.
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
The Numerical Solution Of Ordinary And Partial Differential Equations
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Author : Granville Sewell
language : en
Publisher:
Release Date : 1988
The Numerical Solution Of Ordinary And Partial Differential Equations written by Granville Sewell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Ordinary Differential Equations
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Author : Charles E. Roberts
language : en
Publisher: Prentice Hall
Release Date : 1979
Ordinary Differential Equations written by Charles E. Roberts and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains
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Author : Feliz Manuel Minhos
language : en
Publisher: World Scientific
Release Date : 2022-04-11
Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains written by Feliz Manuel Minhos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-11 with Mathematics categories.
Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.
Differential Equations Chaos And Variational Problems
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Author : Vasile Staicu
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-12
Differential Equations Chaos And Variational Problems written by Vasile Staicu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-12 with Mathematics categories.
This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.
Recent Investigations Of Differential And Fractional Equations And Inclusions
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Author : Snezhana Hristova
language : en
Publisher: MDPI
Release Date : 2021-02-22
Recent Investigations Of Differential And Fractional Equations And Inclusions written by Snezhana Hristova and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of fractional differential equations.
New Trends In Differential And Difference Equations And Applications
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Author : Feliz Manuel Minhós
language : en
Publisher: MDPI
Release Date : 2019-10-14
New Trends In Differential And Difference Equations And Applications written by Feliz Manuel Minhós and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-14 with Mathematics categories.
This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.
Handbook Of Exact Solutions For Ordinary Differential Equations
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Author : Valentin F. Zaitsev
language : en
Publisher: CRC Press
Release Date : 2002-10-28
Handbook Of Exact Solutions For Ordinary Differential Equations written by Valentin F. Zaitsev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-28 with Mathematics categories.
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo