Topological and Variational Methods for Nonlinear Boundary Value Problems PDF Download
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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: Yihong Du
Publisher: World Scientific
ISBN: 9812566244
Category : Mathematics
Languages : en
Pages : 202
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Book Description
The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
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: 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: Leszek Gasinski
Publisher: CRC Press
ISBN: 1420035037
Category : Mathematics
Languages : en
Pages : 790
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Book Description
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.
Author: Wolodymyr V. Petryshyn
Publisher: Cambridge University Press
ISBN: 0521444748
Category : Mathematics
Languages : en
Pages : 252
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Book Description
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.
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: Zdzislaw Denkowski
Publisher: Springer Science & Business Media
ISBN: 9780306474569
Category : Computers
Languages : en
Pages : 844
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Book Description
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.
Author: L Magalhaes
Publisher: World Scientific
ISBN: 9814545074
Category :
Languages : en
Pages : 578
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Book Description
In this volume, leading experts on differential equations address recent advances in the fields of ordinary differential equations and dynamical systems, partial differential equations and calculus of variations, and their related applications.
Author: Donal O'Regan
Publisher: CRC Press
ISBN: 9780203216491
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Author: C.V. Pao
Publisher: Springer Science & Business Media
ISBN: 1461530342
Category : Mathematics
Languages : en
Pages : 786
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Book Description
In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
