Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 259, pp. 1-12.

Title: Existence of solutions for fractional Hamiltonian systems

Author: Cesar Torres (Univ. de Chile, Santiago, Chile)

Abstract:
 In this work we  prove the existence of solutions for the
 fractional differential equation
 $$
 _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) + L(t)u(t)
 =  \nabla W(t,u(t)),\quad 
 u\in H^{\alpha}(\mathbb{R}, \mathbb{R}^{N}).
 $$
 where $\alpha \in (1/2, 1)$.
 Assuming L is coercive at infinity we show that this equation
 has at least one nontrivial solution.

Submitted June 10, 2013. Published November 26, 2013.
Math Subject Classifications: 26A33, 34C37, 35A15, 35B38.
Key Words: Liouville-Weyl fractional derivative; fractional Hamiltonian systems;
           critical point; variational methods.