Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems

Variational problems are part of our classical cultural heritage. The book gives an introduction to variational methods and presents on overview of areas of current research in this field. Particular topics included are the direct methods including lower semi-continuity results, the compensated compactness method, the concentration compactness method, Ekeland's variational principle, and duality methods or minimax methods, including the mountain pass theorems, index theory, perturbation theory, linking and extensions of these techniques to non-differentiable functionals and functionals defined on convex sets - and limit cases. All results are illustrated by specific examples, involving Hamiltonian systems, non-linear elliptic equations and systems, and non-linear evolution problems. These examples often represent the current state of the art in their fields and open perspective for further research. Special emphasis is laid on limit cases of the Palais-Smale condition.