In this paper, we study the existence of infinitely many periodic solutions
for second order Hamiltonian systems uΒ¨+βuβV(t,u)=0, where V(t,u) is either asymptotically quadratic or superquadratic as β£uβ£ββ.Comment: to appear in JDE(doi:10.1016/j.jde.2011.05.021