Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems

We study the existence of homoclinic orbits for first order time-dependent Hamiltonian systems ż=JHz(z, t), where H(z, t) depends periodically on t and Hz(z, t) is asymptotically linear in z as |z|→∞. We also consider an asymptotically linear Schrödinger equation in RN.