Infinitely many periodic solutions for second order Hamiltonian systems

In this paper, we study the existence of infinitely many periodic solutions for second order Hamiltonian systems $\ddot{u}+{\mathrm{\nabla }}_{u}V(t,u)=0$, where $V(t, u)$iseitherasymptoticallyquadraticorsuperquadraticas$|u|\to \infty$.