Solutions for subquadratic fractional Hamiltonian systems without coercive conditions

Abstract

In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systems urn:x-wiley:1704214:media:mma3031:mma3031-math-0001 where α ∈ (1 ∕ 2,1), , , is a symmetric and positive definite matrix for all , , and ∇ W is the gradient of W at u . The novelty of this paper is that, assuming L is bounded in the sense that there are constants 0 < τ 1 < τ 2 < + ∞ such that τ 1 | u | 2 ≤ ( L ( t ) u , u ) ≤ τ 2 | u | 2 for all 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 [Z. Zhang and R. Yuan, Variational approach to solutions for a class of fractional Hamiltonian systems, Math. Methods Appl. Sci., DOI:10.1002/mma.2941] are generalized and significantly improved. Copyright © 2014 John Wiley & Sons, Ltd.