LEADER 03814oam 2200649 450 001 9910714153503321 005 20220627052128.0 010 $a1-4612-4146-4 024 7 $a10.1007/978-1-4612-4146-1 035 $a(CKB)3400000000090723 035 $a(SSID)ssj0001297660 035 $a(PQKBManifestationID)11866311 035 $a(PQKBTitleCode)TC0001297660 035 $a(PQKBWorkID)11230320 035 $a(PQKB)11309928 035 $a(DE-He213)978-1-4612-4146-1 035 $a(MiAaPQ)EBC3075887 035 $a(MiAaPQ)EBC6494642 035 $a(PPN)238039153 035 $a(OCoLC)959982839 035 $a(OCoLC)993400000000090723 035 $a(EXLCZ)993400000000090723 100 $a20210805d1996 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMinimax theorems /$fMichel Willem 205 $a1st ed. 1996. 210 1$aBoston, Massachusetts :$cBirkhäuser,$d[1996] 210 4$d©1996 215 $a1 online resource (X, 165 p.) 225 1 $aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v24 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-8176-3913-6 311 $a1-4612-8673-5 320 $aIncludes bibliographical references (pages [153]-159) and indexes. 327 $a1 Mountain pass theorem -- 1.1 Differentiable functionals -- 1.2 Quantitative deformation lemma -- 1.3 Mountain pass theorem -- 1.4 Semilinear Dirichlet problem -- 1.5 Symmetry and compactness -- 1.6 Symmetric solitary waves -- 1.7 Subcritical Sobolev inequalities -- 1.8 Non symmetric solitary waves -- 1.9 Critical Sobolev inequality -- 1.10 Critical nonlinearities -- 2 Linking theorem -- 2.1 Quantitative deformation lemma -- 2.2 Ekeland variational principle -- 2.3 General minimax principle -- 2.4 Semilinear Dirichlet problem -- 2.5 Location theorem -- 2.6 Critical nonlinearities -- 3 Fountain theorem -- 3.1 Equivariant deformation -- 3.2 Fountain theorem -- 3.3 Semilinear Dirichlet problem -- 3.4 Multiple solitary waves -- 3.5 A dual theorem -- 3.6 Concave and convex nonlinearities -- 3.7 Concave and critical nonlinearities -- 4 Nehari manifold -- 4.1 Definition of Nehari manifold -- 4.2 Ground states -- 4.3 Properties of critical values -- 4.4 Nodal solutions -- 5 Relative category -- 5.1 Category -- 5.2 Relative category -- 5.3 Quantitative deformation lemma -- 5.4 Minimax theorem -- 5.5 Critical nonlinearities -- 6 Generalized linking theorem -- 6.1 Degree theory -- 6.2 Pseudogradient flow -- 6.3 Generalized linking theorem -- 6.4 Semilinear Schrödinger equation -- 7 Generalized Kadomtsev-Petviashvili equation -- 7.1 Definition of solitary waves -- 7.2 Functional setting -- 7.3 Existence of solitary waves -- 7.4 Variational identity -- 8 Representation of Palais-Smale sequences -- 8.1 Invariance by translations -- 8.2 Symmetric domains -- 8.3 Invariance by dilations -- 8.4 Symmetric domains -- Appendix A: Superposition operator -- Appendix B: Variational identities -- Appendix C: Symmetry of minimizers -- Appendix D: Topological degree -- Index of Notations. 410 0$aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v24 606 $aBoundary value problems 606 $aMathematical physics 606 $aMaxima and minima 615 0$aBoundary value problems. 615 0$aMathematical physics. 615 0$aMaxima and minima. 676 $a515.64 700 $aWillem$b Michel$0344839 701 $aFan$b Ky$054069 712 02$aUnited States.$bNational Bureau of Standards. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910714153503321 996 $aMinimax theorems$93451914 997 $aUNINA