Minimax Theorems
Birkhauser Boston Inc (Verlag)
978-0-8176-3913-6 (ISBN)
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.
| Reihe/Serie | Progress in Nonlinear Differential Equations and Their Applications ; 24 |
|---|---|
| Zusatzinfo | X, 165 p. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 0-8176-3913-6 / 0817639136 |
| ISBN-13 | 978-0-8176-3913-6 / 9780817639136 |
| Zustand | Neuware |
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