03814oam 2200649 450 991071415350332120220627052128.01-4612-4146-410.1007/978-1-4612-4146-1(CKB)3400000000090723(SSID)ssj0001297660(PQKBManifestationID)11866311(PQKBTitleCode)TC0001297660(PQKBWorkID)11230320(PQKB)11309928(DE-He213)978-1-4612-4146-1(MiAaPQ)EBC3075887(MiAaPQ)EBC6494642(PPN)238039153(OCoLC)959982839(OCoLC)993400000000090723(EXLCZ)99340000000009072320210805d1996 uy 0engurnn#008mamaatxtccrMinimax theorems /Michel Willem1st ed. 1996.Boston, Massachusetts :Birkhäuser,[1996]©19961 online resource (X, 165 p.)Progress in Nonlinear Differential Equations and Their Applications,1421-1750 ;24Bibliographic Level Mode of Issuance: Monograph0-8176-3913-6 1-4612-8673-5 Includes bibliographical references (pages [153]-159) and indexes.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.Progress in Nonlinear Differential Equations and Their Applications,1421-1750 ;24Boundary value problemsMathematical physicsMaxima and minimaBoundary value problems.Mathematical physics.Maxima and minima.515.64Willem Michel344839Fan Ky54069United States.National Bureau of Standards.MiAaPQMiAaPQUtOrBLWBOOK9910714153503321Minimax theorems3451914UNINA