Overview

Devoted to minimax theorems and their applications to partial differential equations, this text presents these theorems in a simple and unified way, starting from a quantitative deformation lemma. Many applications are given to problems dealing with lack of compactness, especially problems with critical exponents and existence of solitary waves. There are also recent results and some unpublished material, such as a treatment of the generalized Kadomtsev-Petviashvili equation.

Full Product Details

Author:   Michel Willem
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1996 ed.
Volume:   24
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.950kg
ISBN:  

9780817639136

ISBN 10:   0817639136
Pages:   165
Publication Date:   01 February 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Mountain pass theorem.- 1.1 Differentiable functionals.- 1.2 Quantitative deformation lemma.- 1.3 Mountain pass theorem.- 1.4 Semilinear Dirichlet problem.- 1.5 Symmetry and compactness.- 1.6 Symmetric solitary waves.- 1.7 Subcritical Sobolev inequalities.- 1.8 Non symmetric solitary waves.- 1.9 Critical Sobolev inequality.- 1.10 Critical nonlinearities.- 2 Linking theorem.- 2.1 Quantitative deformation lemma.- 2.2 Ekeland variational principle.- 2.3 General minimax principle.- 2.4 Semilinear Dirichlet problem.- 2.5 Location theorem.- 2.6 Critical nonlinearities.- 3 Fountain theorem.- 3.1 Equivariant deformation.- 3.2 Fountain theorem.- 3.3 Semilinear Dirichlet problem.- 3.4 Multiple solitary waves.- 3.5 A dual theorem.- 3.6 Concave and convex nonlinearities.- 3.7 Concave and critical nonlinearities.- 4 Nehari manifold.- 4.1 Definition of Nehari manifold.- 4.2 Ground states.- 4.3 Properties of critical values.- 4.4 Nodal solutions.- 5 Relative category.- 5.1 Category.- 5.2 Relative category.- 5.3 Quantitative deformation lemma.- 5.4 Minimax theorem.- 5.5 Critical nonlinearities.- 6 Generalized linking theorem.- 6.1 Degree theory.- 6.2 Pseudogradient flow.- 6.3 Generalized linking theorem.- 6.4 Semilinear Schrödinger equation.- 7 Generalized Kadomtsev-Petviashvili equation.- 7.1 Definition of solitary waves.- 7.2 Functional setting.- 7.3 Existence of solitary waves.- 7.4 Variational identity.- 8 Representation of Palais-Smale sequences.- 8.1 Invariance by translations.- 8.2 Symmetric domains.- 8.3 Invariance by dilations.- 8.4 Symmetric domains.- Appendix A: Superposition operator.- Appendix B: Variational identities.- Appendix C: Symmetry of minimizers.- Appendix D: Topological degree.- Index of Notations.

Reviews

"""The material is presented in a unified way, and the proofs are concise and elegant... Essentially self-contained."" --Mathematical Reviews"

The material is presented in a unified way, and the proofs are concise and elegant... Essentially self-contained. --Mathematical Reviews

The material is presented in a unified way, and the proofs are concise and elegant... Essentially self-contained. --Mathematical Reviews

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