Homoclinic solutions for second order discrete Hamiltonian systems with superquadratic potentials

In this paper, we investigate the existence of homoclinic solutions for the second order self-adjoint discrete Hamiltonian system where , and are neither autonomous nor periodic in n. By using a standard version of the Mountain Pass theorem, we give some new criteria to guarantee that the above system has at least one non-trivial homoclinic solution under the assumption that satisfies more general superquadratic condition. Some recent results are generalized and significantly improved.