Minimax theorems
Author(s)
Bibliographic Information
Minimax theorems
（Progress in nonlinear differential equations and their applications / editor, Haim Brezis, v. 24）
Birkhäuser, 1996
- : us
- : sz
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Note
Bibliography: p. [153]-159
Includes index
Description and Table of Contents
- Volume
-
: us ISBN 9780817639136
Description
Many boundary value problems are equivalent to Au=O (1) where A : X ---+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional 0 and e E X such that lIell > rand inf
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 Schroedinger 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.
- Volume
-
: sz ISBN 9783764339135
Description
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.
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