Variational approach to solutions for a class of fractional Hamiltonian systems

In this paper, we investigate the existence of infinitely many solutions for the following fractional Hamiltonian systems: {tD(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 alpha is an element of (1.2,t), t is an element of R, u is an element of R-n, and L is an element of C(R,R-n2) are symmetric and positive definite matrices for all t is an element of R, W is an element of C-1(R x R-n,R), and del W is the gradient of W at u. The novelty of this paper is that, assuming L is coercive at infinity, and W is of subquadratic growth as vertical bar u vertical bar -> +infinity, we show that (FHS) possesses infinitely many solutions via the genus properties in the critical theory. Recent results in the literature are generalized and significantly improved. Copyright (C) 2013 JohnWiley & Sons, Ltd.