Periodic solutions of some non-autonomous second order Hamiltonian systems

In this paper, we study the existence of periodic solutions of some non-autonomous second order Hamiltonian systems {ü(t)=∇F(t,u(t)),a.e.t∈[0,T],u(0)−u(T)=u̇(0)−u̇(T)=0. We obtain some new existence theorems by the least action principle.