Nonlinear analysis and semilinear elliptic problems / Antonio Ambrosetti, Andrea Malchiodi.

Format:

Book

Author/Creator:

Ambrosetti, A. (Antonio), author.

Malchiodi, Andrea, author.

Series:

Cambridge studies in advanced mathematics ; 104.

Cambridge studies in advanced mathematics ; 104

Language:

English

Subjects (All):

Nonlinear theories.

Differential equations, Elliptic.

Physical Description:

1 online resource (xi, 316 pages) : digital, PDF file(s).

Other Title:

Nonlinear Analysis & Semilinear Elliptic Problems

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Language Note:

English

Summary:

Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.

Contents:

Cover; Half-title; Series-title; Title; Copyright; Contents; Preface; 1 Preliminaries; 1.1 Differential calculus; 1.2 Function spaces; 1.3 Nemitski operators; 1.4 Elliptic equations; PART I Topological methods; 2 A primer on bifurcation theory; 3 Topological degree, I; 4 Topological degree, II: global properties; PART II Variational methods, I; 5 Critical points: extrema; 6 Constrained critical points; 7 Deformations and the Palais-Smale condition; 8 Saddle points and min-max methods; PART III Variational methods, II; 9 Lusternik-Schnirelman theory

10 Critical points of even functionals on symmetric manifolds11 Further results on elliptic Dirichlet problems; 12 Morse theory; PART IV Appendices; Appendix 1 Qualitative results; Appendix 2 The concentration compactness principle; Appendix 3 Bifurcation for problems on Rn; Appendix 4 Vortex rings in an ideal fluid; Appendix 5 Perturbation methods; Appendix 6 Some problems arising in differential geometry; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 309-314) and index.

ISBN:

1-107-16886-4

1-280-75062-6

9786610750627

0-511-26971-4

0-511-27027-5

0-511-26866-1

0-511-31943-6

0-511-61826-3

0-511-26868-8

OCLC:

166432889