SUBHARMONIC SOLUTIONS FOR A CLASS OF LAGRANGIAN SYSTEMS

We prove that second order Hamiltonian systems -(u) over dot = V-u(t,u) with a potential V: R x R-N -> R of class C-1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [14]. Indeed, we weaken the latter condition in a neighbourhood of 0 is an element of R-N. We will also discuss when subharmonics pass to a nontrivial homoclinic orbit.