Infinitely Many Homoclinic Orbits for Hamiltonian Systems with Group Symmetries

Abstract

<p>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</p> <pre>ż = JH_z(t, z)</pre> <p>without any periodicity assumption on H, providing that H(t, z) is G-symmetric with respect to z ∈ R^2N, is superquadratic as |z| → ∞, and satisfies some additional assumptions.</p>