Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
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...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2008, 2008
|
| Edition: | 4th ed. 2008 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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