HOMOCLINIC SOLUTIONS NEAR THE ORIGIN FOR A CLASS OF FIRST ORDER HAMILTONIAN SYSTEMS

摘要

In this paper,we study the existence of infinitely many homoclinic solutions for a class of first order Hamiltonian systems ż=J H_(z)(t,z),where the Hamiltonian function H possesses the form H(t,z)=1/2L(t)z⋅z+G(t,z),and G(t,z)is only locally defined near the origin with respect to z.Under some mild conditions on L and G,we show that the existence of a sequence of homoclinic solutions is actually a local phenomenon in some sense,which is essentially forced by the subquadraticity of G near the origin with respect to z.