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
Inhaltsverzeichnis
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.
