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: ( FHS ) where α ∈ (1 ∕ 2,1), , , and are symmetric and positive definite matrices for all , , and ? 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 | u | → + ∞ , 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 © 2013 John Wiley & Sons, Ltd.