Homoclinic orbits for a class of first order nonperiodic Hamiltonian systems

In this paper we study the existence of infinitely many homoclinic orbits for a class of first order Hamiltonian systems ż=JHz(t,z), where the Hamiltonian function H(t,z) is nonperiodic in t and only locally defined near the origin with respect to z. Under some mild conditions on H, we show that these Hamiltonian systems possess a sequence of homoclinic orbits near the origin.