Second order nonautonomous systems with symmetric potential changing sign

Abstract

In this paper we deal with the problem of multiplicity of periodic solutions for a class of nonautonomous second order Hamiltonian systems, having indefinite potential. In the particular case that the quadratic part of the potential is negative definite, one reaches a result of subharmonic and homoclinic solutions. The proof of the multiplicity results is based on the Ljusternik-Schnirelmam category theory; the subharmonic solutions are obtained through the constrained minima of the functional to a suitable manifold, and the homoclinics are obtained with a limit procedure starting by the sequence of subharmonics.

Keywords

• hamiltonian systems
• periodic solutions
• subharmonics