Nontrivial Periodic Solutions for Asymptotically Linear Hamiltonian Systems with Resonance

In this paper, we establish some existence results of nontrivial 1-periodic solutions to the first-order asymptotically linear Hamiltonian systems, under the assumptions that the linear operators have different Maslove indices at the origin and at infinity. The results obtained in this paper are also valued for the case that both of the asymptotic matrices may be degenerate (resonant-type) and time dependent.