EXISTENCE OF SOLUTIONS TO FRACTIONAL HAMILTONIAN SYSTEMS WITH LOCAL SUPERQUADRATIC CONDITIONS

In this article, we study the existence of solutions for the fractional Hamiltonian system t D-infinity(alpha) ((-infinity)D(t)(alpha)u(t)) + L(t)u(t) = del W(t, u(t)), u is an element of H-alpha(R,R-N), where D-t(infinity)alpha and D--infinity(t)alpha are the Liouville-Weyl fractional derivatives of order 1=2 < alpha < 1, L is an element of C(R, R-N (x) (N)) is a symmetric matrix-valued function, which is unnecessarily required to be coercive, and W is an element of C-1(R x R-N,R) satisfies some kind of local superquadratic conditions, which is rather weaker than the usual Ambrosetti-Rabinowitz condition.