Struwe M. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

Springer, 2007, 302p., 4th edition.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
Pohoˇzaev’s Non-existence Result
The Brezis-Nirenberg Result
The Effect of Topology
The Yamabe Problem
The Dirichlet Problem for the Equation of Constant Mean Curvature
Harmonic Maps of Riemannian Surfaces