Infinitely many homoclinic orbits for supperlinear Hamiltonian systems

Abstract

In this paper we study the first order nonautonomous Hamiltonian system $$ \dot{z}=\mathcal J H_{z}(t,z), $$ where $H(t,z)$ depends periodically on $t$. By using a generalized linking theorem for strongly indefinite functionals, we prove that the system has infinitely many homoclinic orbits for weak superlinear cases.