Infinitely many periodic solutions for second order Hamiltonian systems

Abstract

In this paper, we study the existence of infinitely many periodic solutions for second order Hamiltonian systems $\ddot{u}+\nabla_u V(t,u)=0$, where $V(t, u)$ is either asymptotically quadratic or superquadratic as $|u|\to \infty$.Comment: to appear in JDE(doi:10.1016/j.jde.2011.05.021