Infinitely many solutions for a class of fractional Hamiltonian systems via critical point theory

In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systemstD ∞ α( − ∞D t α u ( t ) ) + L ( t ) u ( t ) = ∇ W ( t , u ( t ) ) ,u ∈ H α ( R , R n ) ,where α ∈ ( 1 / 2 , 1 ) , u ∈ R N , L ∈ C ( R , R N × N ) , and W ∈ C 1 ( R × R N , R ) . The novelty of this paper is that, relaxing the conditions on the potential function W ( t , x ), we obtain infinitely many solutions via critical point theory. Our results generalize and improve some existing results in the literature. Copyright © 2015 John Wiley & Sons, Ltd.