Periodic solutions for asymptotically linear Hamiltonian system with resonance both at infinity and origin via computation of critical groups

In this paper, we study the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian system which has the same linear term both at infinity and origin. By computation of critical groups at origin and infinity associated with Maslov-type index, we establish the existence for nontrivial periodic solution of the system. Moreover, some conditions employed for the computation of critical groups are weakened.