Infinitely many homoclinic solutions for second-order discrete Hamiltonian systems

In this paper, we study the second-order self-adjoint discrete Hamiltonian system Delta[p(n)Delta u(n - 1)] - L9n)u(n) + del W(n, u(n)) = 0, for all n is an element of Z, where p(n) is an N X N real symmetric positive definite matrix for all n is an element of Z, L : Z -> R-NxN is unnecessarily positive definite for all n is an element of Z and W(n, x) is indefinite sign. By using fountain theorem, we establish some new criteria to guarantee that the above system has infinitely many homoclinic solutions under the assumption that W(n, x) is superquadratic as vertical bar x vertical bar -> + infinity. Our results generalize and improve some existing results in the literature.