Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems /

• Main Author: Struwe, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; 34
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; System theory.; Calculus of variations.; Systems Theory, Control.; Calculus of Variations and Optimal Control; Optimization.; Analysis.

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of th...

Table of Contents:

• The Direct Methods in the Calculus of Variations
• Lower Semi-Continuity
• Constraints
• Compensated Compactness
• The Concentration-Compactness Principle
• Ekeland's Variational Principle
• Duality
• Minimization Problems Depending on Parameters
• Minimax Methods
• The Finite Dimensional Case
• The Palais-Smale Condition
• A General Deformation Lemma
• The Minimax Principle
• Index Theory
• The Mountain Pass Lemma and its Variants
• Perturbation Theory
• Linking
• Parameter Dependence
• Critical Points of Mountain Pass Type
• Non-Differentiable Functionals
• Ljusternik-Schnirelman Theory on Convex Sets
• Limit Cases of the Palais-Smale Condition
• Pohozaev's Non-Existence Result
• The Brezis-Nierenberg Result
• The Effect of Topology
• The Yamabe Problem
• The Dirichlet Problem for the Equation of Constant Mean Curvature
• Harmonic Maps of Riemannian Surfaces
• Appendix A
• Appendix B
• Appendix C
• References
• Index.