Existence of infinitely many homoclinic orbits for nonperiodic superquadratic Hamiltonian systems

In this paper, we study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H(t,z)H(t,z) is superquadratic in z∈R2Nz∈R2N as |z|→∞|z|→∞. By applying a generalized linking theorem for strongly indefinite functionals, we obtain infinitely many homoclinic orbits for the above system.