An introduction to nonlinear functional analysis and elliptic problems
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 pri…
Read More ↓Title Statements
- Full title :An introduction to nonlinear functional analysis and elliptic problems / Antonio Ambrosetti, David Arcoya.
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.
Read More ↓Edition Statements
- Publication Date:©2011.
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Cambridge, Mass
- Language:eng
- Publication Date:©2011.
The Physical Object
- Description:1 online resource (xii, 209 pages)
Edition Identifiers
- ISBN:9780817681142, 0817681140
- DOI:10.1007/978-0-8176-8114-2
- oclc:ocn748519179
- LC Classification:QA377
- Dewey Decimal:515/.3533
Table of 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.
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