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Author Ambrosetti, A. (Antonio)

Title An introduction to nonlinear functional analysis and elliptic problems / Antonio Ambrosetti, David Arcoya
Published Cambridge, Mass. : Birkhäuser, [2011]
Online access available from:
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Description 1 online resource (xii, 209 pages)
Series Progress in nonlinear differential equations and their applications ; vol. 82
Progress in nonlinear differential equations and their applications ; v. 82
Contents Notation -- Preliminaries -- Some Fixed Point Theorems -- Local and Global Inversion Theorems -- Leray-Schauder Topological Degree -- An Outline of Critical Points -- Bifurcation Theory -- Elliptic Problems and Functional Analysis -- Problems with A Priori Bounds -- Asymptotically Linear Problems -- Asymmetric Nonlinearities -- Superlinear Problems -- Quasilinear Problems -- Stationary States of Evolution Equations -- Appendix A Sobolev Spaces -- Exercises -- Index -- Bibliography
Summary This self-contained textbook provides the basic, abstract¡tools¡used in¡nonlinear analysis¡and their applications to semilinear elliptic boundary value problems.¡By first¡outlining the advantages and disadvantages of each method, this comprehensive text¡displays how various¡approaches¡can easily be¡applied¡to a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problems¡is divided into two parts: the first discusses key¡results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray-Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems.¡ The exposition is driven by numerous prototype problems and exposes a variety of approaches to¡solving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a¡practical text for an introductory course or seminar on nonlinear functional analysis
Bibliography Includes bibliographical references (pages 193-196) and index
Subject Differential equations, Elliptic.
Nonlinear functional analysis.
Form Electronic book
Author Arcoya, David.
ISBN 0817681140 (electronic bk.)
9780817681142 (electronic bk.)