A generalized saddle point theorem

Abstract

The well-known saddle point theorem is extended to the case of functions defined on a product space X × V, where X is a Banach space and V is a compact manifold. Under some linking conditions, the existence of at least cuplength ( V) + 1 critical points is proved. The abstract theorems are applied to the existence problems of periodic solutions of Hamiltonian systems with periodic nonlinearity and/or resonance.