Chapter Ⅰ.The Direct Methods in the Calculus of Variations
1.Lower Semi-Continuity
2.Constraints
3.Compensated Compactness
4.The Concentration-Compactness Principle
5.Ekeland's Variational Principle
6.Duality
7.Minimization Problems Depending on Parameters
Chapter Ⅱ.Minimax Methods
1.The Finite Dimensional Case
2.The Palais-Smale Condition
3.A General Deformation Lemma
4.The Minimax Principle
5.Index Theory
6.The Mountain Pass Lemma and its Variants
7.Perturbation Theory
8.Linking
9.Parameter Dependence
10.Critical Points of Mountain Pass Type
l1 Non—Differentiable Functionals
12.Ljusternik—Schnirelman Theory on Convex Sets
Chapter Ⅲ.Limit Cases of the Palais—Smale Condition
1.Pohoaev’S Non—Existence Result
2.The Brezis—Nirenberg Result
3.The Effect of Topology
4.The Yamabe Problem
5.The Dirichlet Problem for the Equation of Constant Mean Curvature
6.Harmonic Maps of Riemannian Surfaces
Appendix A
Appendix B
Appendix C
References
Index
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