Infinitely Many Solutions for Fractional Hamiltonian Systems with Locally Defined Potentials

In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian where −∞ Dtα and t Dα∞ are left and right Liouville-Weyl fractional derivatives of order 1 < α < 1 on the whole axis respectively, 2 L ∈C(R,RN2) is a symmetric matrix valued function unnecessary coercive and W(t,x) ∈C1(R×RN,R). The novelty of this paper is that, assuming that L is bounded from below and unnecessarily coercive at infinity, and W is only locally defined near the origin with respect to the second variable, we show that (1) possesses infinitely many solutions via a variant Symmetric Mountain Pass Theorem.