Topological Degree Methods In Nonlinear Boundary Value Problems
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Topological Degree Methods In Nonlinear Boundary Value Problems
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Author : J. Mawhin
language : en
Publisher: American Mathematical Soc.
Release Date : 1979
Topological Degree Methods In Nonlinear Boundary Value Problems written by J. Mawhin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many aspects of the modern theory of nonlinear differential equations and the theory of nonlinear analysis.
Topological Degree Methods In Nonlinear Boundary Value Problems
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Author : Jean Mawhin
language : en
Publisher:
Release Date : 1977
Topological Degree Methods In Nonlinear Boundary Value Problems written by Jean Mawhin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Topological Methods In The Study Of Boundary Value Problems
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Author : Pablo Amster
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-23
Topological Methods In The Study Of Boundary Value Problems written by Pablo Amster 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 2013-10-23 with Mathematics categories.
This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.
Nonsmooth Critical Point Theory And Nonlinear Boundary Value Problems
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Author : Leszek Gasinski
language : en
Publisher: CRC Press
Release Date : 2004-07-27
Nonsmooth Critical Point Theory And Nonlinear Boundary Value Problems written by Leszek Gasinski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-27 with Mathematics categories.
Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.
Generalized Topological Degree And Semilinear Equations
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Author : Wolodymyr V. Petryshyn
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-29
Generalized Topological Degree And Semilinear Equations written by Wolodymyr V. Petryshyn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-29 with Mathematics categories.
This book describes many new results and extensions of the theory of generalized topological degree for densely defined A-proper operators and presents important applications, particularly to boundary value problems of nonlinear ordinary and partial differential equations that are intractable under any other existing theory. A-proper mappings arise naturally in the solution to an equation in infinite dimensional space via the finite dimensional approximation. The theory subsumes classical theory involving compact vector fields as well as the more recent theories of condensing vector-fields, strongly monotone, and strongly accretive maps. Researchers and graduate students in mathematics, applied mathematics, and physics who make use of nonlinear analysis will find this an important resource for new techniques.
The Duffing Equation
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Author : Lakshmi Burra
language : en
Publisher: Springer Nature
Release Date : 2025-01-03
The Duffing Equation written by Lakshmi Burra and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-03 with Mathematics categories.
This book discusses the generalized Duffing equation and its periodic perturbations, with special emphasis on the existence and multiplicity of periodic solutions, subharmonic solutions and different approaches to prove rigorously the presence of chaotic dynamics. Topics in the book are presented at an expository level without entering too much into technical detail. It targets to researchers in the field of chaotic dynamics as well as graduate students with a basic knowledge of topology, analysis, ordinary differential equations and dynamical systems. The book starts with a study of the autonomous equation which represents a simple model of dynamics of a mechanical system with one degree of freedom. This special case has been discussed in the book by using an associated energy function. In the case of a centre, a precise formula is given for the period of the orbit by studying the associated period map. The book also deals with the problem of existence of periodic solutions for the periodically perturbed equation. An important operator, the Poincaré map, is introduced and studied with respect to the existence and multiplicity of its fixed points and periodic points. As a map of the plane into itself, complicated structure and patterns can arise giving numeric evidence of the presence of the so-called chaotic dynamics. Therefore, some novel topological tools are introduced to detect and rigorously prove the existence of periodic solutions as well as analytically prove the existence of chaotic dynamics according to some classical definitions introduced in the last decades. Finally, the rest of the book is devoted to some recent applications in different mathematical models. It carefully describes the technique of “stretching along the paths”, which is a very efficient tool to prove rigorously the presence of chaotic dynamics.
Theory Of Singular Boundary Value Problems
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Author : Donal O'regan
language : en
Publisher: World Scientific
Release Date : 1994-04-29
Theory Of Singular Boundary Value Problems written by Donal O'regan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-29 with Mathematics categories.
This book surveys some topics in the rapidly developing areas of regular and singular boundary value problems. It also provides a detailed account of the current state of the literature on existence theory for ordinary differential equations. Results are presented for finite and semi-infinite intervals. Singularities in both independent and dependent variables are discussed.
An Introduction To Nonlinear Analysis Applications
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Author : Zdzislaw Denkowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-31
An Introduction To Nonlinear Analysis Applications written by Zdzislaw Denkowski 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 2003-01-31 with Computers categories.
This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.
Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan 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 2013-04-17 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Stability And Bifurcation Theory For Non Autonomous Differential Equations
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Author : Anna Capietto
language : en
Publisher: Springer
Release Date : 2012-12-14
Stability And Bifurcation Theory For Non Autonomous Differential Equations written by Anna Capietto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.