Infinitely Many Solutions for Fractional Hamiltonian Systems with Locally Defined Potentials

Abstract

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.