Existence of solutions for superquadratic or asymptotically quadratic fractional Hamiltonian systems

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.