In this work we prove the existence of solution for a class of perturbed fractional Hamiltonian systems given by \begin{ eqnarray}\label{ eq00} -{ _{ t}}D_{ \infty}^{ \alpha}(_{ -\infty}D_{ t}^{ \alpha}u(t)) - L(t)u(t) + \nabla W(t,u(t)) = f(t), \end{ eqnarray} where $\alpha \in (1/2, 1)$, $t\in \mathbb{ R}$, $u\in \mathbb{ R}^{ n}$, $L\in C(\mathbb{ R}, \mathbb{ R}^{ n^{ 2}})$ is a symmetric and positive definite matrix for all $t\in \mathbb{ R}$, $W\in C^{ 1}(\mathbb{ R}\times \mathbb{ R}^{ n}, \mathbb{ R})$ and $\nabla W$ is the gradient of $W$ at $u$. The novelty of this paper is that, assuming $L$ is coercive at infinity we show that (\ref{ eq00}) at least has one nontrivial solution.
Categories: math.AP