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Nonlinear second order elliptic equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear second order elliptic equationsby Mingxin Wang, Peter Y. H. Pang.
Author:	Wang, Mingxin.
other author:	Pang, Peter Y. H.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	xii, 314 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Elliptic.
Online resource:	https://doi.org/10.1007/978-981-99-8692-7
ISBN:	9789819986927$q(electronic bk.)

Nonlinear second order elliptic equations
Wang, Mingxin.

Nonlinear second order elliptic equations[electronic resource] /by Mingxin Wang, Peter Y. H. Pang. - Singapore :Springer Nature Singapore :2024. - xii, 314 p. :ill., digital ;24 cm.

Preface -- Preliminaries -- Eigenvalue problems of second order linear elliptic operators -- Upper and lower solutions method for single equations -- Upper and lower solutions method for systems -- Theory of topological degree in cones and applications -- Systems with homogeneous Neumann boundary conditions -- P-Laplace equations and systems -- Appendix A: Basic results of Sobolev spaces and nonlinear functional analysis -- Appendix B: Basic theory of elliptic equations -- References -- Index.

This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions. While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained. A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who have already had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers.

ISBN: 9789819986927$q(electronic bk.)

Standard No.: 10.1007/978-981-99-8692-7doiSubjects--Topical Terms:

205654
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 515.3533

Nonlinear second order elliptic equations
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505 0 $a Preface -- Preliminaries -- Eigenvalue problems of second order linear elliptic operators -- Upper and lower solutions method for single equations -- Upper and lower solutions method for systems -- Theory of topological degree in cones and applications -- Systems with homogeneous Neumann boundary conditions -- P-Laplace equations and systems -- Appendix A: Basic results of Sobolev spaces and nonlinear functional analysis -- Appendix B: Basic theory of elliptic equations -- References -- Index.
520 $a This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions. While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained. A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who have already had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers.
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