Existence of solution for a class of fractional Hamiltonian systems

Abstract

In this work we want to prove the existence of solution for a class of fractional Hamiltonian systems given by {eqnarray*}_{t}D_{\infty}^α(_{-\infty}D_{t}^αu(t)) + L(t)u(t) = & \nabla W(t,u(t)) u\in H^α(\mathbb{R}, \mathbb{R}^{N}) {eqnarray*}