Minimax theorems / / Michel Willem

• Record Nr.: UNINA9910714153503321
• Autore: Willem Michel
• Pubbl/distr/stampa: Boston, Massachusetts : , : Birkhäuser, , [1996]; ©1996
• ISBN: 1-4612-4146-4
• Edizione: [1st ed. 1996.]
• Descrizione fisica: 1 online resource (X, 165 p.)
• Collana: Progress in Nonlinear Differential Equations and Their Applications, , 1421-1750 ; ; 24
• Altri autori (Persone): FanKy
• Disciplina: 515.64
• Soggetti: Boundary value problems; Mathematical physics; Maxima and minima
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (pages [153]-159) and indexes.
• Nota di contenuto: 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.