Critical point theorem for asymptotically quadratic functional without compactness
The main result of the present paper establishes an abstract critical point theorem for asymptotically quadratic functionals with lack of compactness. The proof follows after a careful analysis of Morse indices of critical points, combined with an adequate penalization technique. A central role is also played by Betti numbers created by singular relative homology groups. This result is applied to study the existence of nontrivial periodic solutions of second order Hamiltonian systems.
scientific article; zbMATH DE number 5757986
scientific article