Periodic solutions of Hamiltonian systems with anisotropic growth

Abstract

In this paper we obtain some existence and multiplicity results for periodic solutions of nonautonomous Hamiltonian systems $\dot z(t)=J\nabla H(z(t),t)$ whose Hamiltonian functions may have simultaneously, in different components, superquadratic, subquadratic and quadratic behaviors. Our results generalize some earlier work [3] of P. Felmer and [5] of P. Felmer and Z.-Q. Wang.