Existence and concentration of solution for a class of fractional Hamiltonian systems with subquadratic potential

In this article, we consider the following fractional Hamiltonian systemswhere , is a parameter, and . Unlike most other papers on this problem, we require that L(t) is a positive semi-definite symmetric matrix for all , that is, is allowed to occur in some finite interval of . Under some mild assumptions on W, we establish the existence of nontrivial weak solution, which vanish on as and converge to in ; here is nontrivial weak solution of the Dirichlet BVP for fractional Hamiltonian systems on the finite interval . Furthermore, we give the multiplicity results for the above fractional Hamiltonian systems.