This work is devoted to the study of subharmonic solutions of a second-order Hamiltonian system
near an equilibrium point, say q = 0. The problem of existence of periodic solutions from the global point of view is also considered.
This problem has been studied for the case where the potential is positive and superquadratic. In this work a potential V that has change in sign is considered. The potential is decomposed as
where P is homogeneous, superquadratic and nondegenerate, and is of higher order near 0. In this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium, such that their minimal periods converge to infinity.
This problem is approached from a variational point of view. Existence of subharmonic and periodic solutions is obtained via minimax techniques.