AuthorWillem, Michel. author
TitleMinimax Theorems [electronic resource] / by Michel Willem
ImprintBoston, MA : Birkhรคuser Boston, 1996
Connect tohttp://dx.doi.org/10.1007/978-1-4612-4146-1
Descript X, 165 p. online resource

CONTENT

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 Schrรถdinger 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


SUBJECT

  1. Mathematics
  2. Applied mathematics
  3. Engineering mathematics
  4. Game theory
  5. Mathematics
  6. Applications of Mathematics
  7. Game Theory
  8. Economics
  9. Social and Behav. Sciences