## A generalized saddle point theorem.(English)Zbl 0682.34032

Summary: The well-known saddle point theorem is extended to the case of functions defined on a product space $$X\times V$$, 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.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 70H05 Hamilton’s equations