Minimax Theorems

Michel Willem (Autor)

Buch | Softcover

165 Seiten

2011 | Softcover reprint of the original 1st ed. 1996
Springer-Verlag New York Inc.
978-1-4612-8673-8 (ISBN)

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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 0 and e E X such that lIell > rand inf

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.

Reihe/Serie	Progress in Nonlinear Differential Equations and Their Applications ; 24
Zusatzinfo	X, 165 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
ISBN-10	1-4612-8673-5 / 1461286735
ISBN-13	978-1-4612-8673-8 / 9781461286738
Zustand	Neuware