Infinitely Many Homoclinic Orbits for Hamiltonian Systems with Group Symmetries

Abstract

This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems ż = JHz(t,z) without any periodicity assumption on H, providing that H(t,z) is G-symmetric with respect to z ∈ R2N, is superquadratic as |z| → ∞, and satisfies some additional assumptions.