Existence of solutions to fractional Hamiltonian systems with local superquadratic conditions

Abstract

In this article, we study the existence of solutions for the fractional Hamiltonian system tDα∞ (-∞Dαtu(t)) + L(t)u(t) = ∇W(t, u(t)), u ∈ Hα (ℝ, ℝN), where tDα∞ and -∞Dαt are the Liouville-Weyl fractional derivatives of order 1/2 < α < 1, L ∈ C (ℝ, ℝNxN) is a symmetric matrix-valued function, which is unnecessarily required to be coercive, and W ∈ C1 (ℝ x ℝN, ℝ) satisfies some kind of local superquadratic conditions, which is rather weaker than the usual Ambrosetti-Rabinowitz condition.