Abstract
In this paper, by the critical point theory, we consider the existence and multiplicity of solutions for the following fractional differential equation tD∞α(−∞Dtαu(t))+L(t)u(t)=∇W(t,u(t)),t∈R, where α∈(12,1], −∞Dtα and tD∞α are left and right Liouville–Weyl fractional derivatives of order α on the whole axis R respectively, u∈Rn, L(t) is positive definite symmetric matrix for all t∈R and W:R×Rn→R is a suitably chosen function.