Existence of solutions for superquadratic or asymptotically quadratic fractional Hamiltonian systems

In this paper, we are concerned with a class of periodic fractional Hamiltonian systems when the Hamiltonian is superquadratic not satisfying the well-known Ambrosetti-Rabinowitz condition or with asymptotically quadratic growth. Using the monotonicity trick of Jeanjean and the concentration compactness principle, we prove the existence of nontrivial solution. Some recent results in the literature are generalized and significantly improved.