Ground state solutions for a class of superquadratic fractional Hamiltonian systems

Consider the following fractional Hamiltonian system {D-t(infinity)alpha((-infinity)D(t)(alpha)u)(t)+L(t)u(t)= del W(t,u(t)),t is an element of Ru is an element of H alpha(R), u is an element of (HR)-R-alpha(), where D-t(infinity)alpha D--infinity(t)alpha are the Liouville-Weyl fractional derivatives of order 1/2<alpha<1, L is an element of C(R,RN2)is a symmetric matrix-valued function and W(t,x)is an element of C1(RxRN,R). We establish the existence of ground state solution for (1) when L is not required to be either uniformly positive definite or coercive and W(t, x) satisfies a kind of superquadratic conditions due to Ding and Luan for Schrodinger equation. The main idea here have lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. Some recent results in the literature are generalized and significantly improved.