Topological Degree Methods in Nonlinear Boundary Value Problems PDF Download
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Author: J. Mawhin
Publisher: American Mathematical Soc.
ISBN: 082181690X
Category : Mathematics
Languages : en
Pages : 130
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Book Description
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.
Author: J. Mawhin
Publisher: American Mathematical Soc.
ISBN: 082181690X
Category : Mathematics
Languages : en
Pages : 130
Get Book Here
Book Description
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.
Author: Dumitru Motreanu
Publisher: Springer Science & Business Media
ISBN: 1461493234
Category : Mathematics
Languages : en
Pages : 465
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Book Description
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
Author: Pavel Drabek
Publisher: CRC Press
ISBN: 9780582309210
Category : Mathematics
Languages : en
Pages : 172
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Book Description
In the rapidly developing area of nonlinear theory of differential equations, many important results have been obtained by the use of nonlinear functional analysis based on topological and variational methods. The survey papers presented in this volume represent the current state of the art in the subject. The methods outlined in this book can be used to obtain new results concerning the existence, uniqueness, multiplicity, and bifurcation of the solutions of nonlinear boundary value problems for ordinary and partial differential equations. The contributions to this volume are from well known mathematicians, and every paper contained in this book can serve both as a source of reference for researchers working in differential equations and as a starting point for those wishing to pursue research in this direction. With research reports in the field typically scattered in many papers within various journals, this book provides the reader with recent results in an accessible form.
Author: Enayet U Tarafdar
Publisher: World Scientific
ISBN: 9814476218
Category : Mathematics
Languages : en
Pages : 627
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Book Description
This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.
Author: Pablo Amster
Publisher: Springer Science & Business Media
ISBN: 1461488931
Category : Mathematics
Languages : en
Pages : 238
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Book Description
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.
Author: Nikola? Iosifovich Ronto
Publisher: World Scientific
ISBN: 9789810236762
Category : Mathematics
Languages : en
Pages : 470
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Book Description
This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory ? namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods.
Author: C. De Coster
Publisher: Elsevier
ISBN: 0080462472
Category : Mathematics
Languages : en
Pages : 502
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Book Description
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Author: Klaus Deimling
Publisher: Courier Corporation
ISBN: 0486132358
Category : Mathematics
Languages : en
Pages : 466
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Book Description
This text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. 1985 edition.
Author: Manuel Delgado
Publisher: World Scientific
ISBN: 981238765X
Category : Mathematics
Languages : en
Pages : 266
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Book Description
The work of Jean Mawhin covers different aspects of the theory of differential equations and nonlinear analysis. On the occasion of his sixtieth birthday, a group of mathematicians gathered in Sevilla, Spain, in April 2003 to honor his mathematical achievements as well as his unique personality.This book provides an extraordinary view of a number of ground-breaking ideas and methods in nonlinear analysis and differential equations.List of Contributors: H Amann, M Delgado, J L G mez, A M Krasnoselskij, E Liz, J Mawhin, P Quittner, B P Rynne, L Sanchez, K Schmitt, J R Ward, F Zanolin, and others.
Author: Donal O'Regan
Publisher: Springer Science & Business Media
ISBN: 9401715173
Category : Mathematics
Languages : en
Pages : 207
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Book Description
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.
