Homoclinic orbits for asymptotically linear discrete Hamiltonian systems.

We study the existence of homoclinic solutions for the following second-order self-adjoint discrete Hamiltonian system: $\triangle[p(n)\triangle u(n-1)]-L(n)u(n)+\nabla W(n, u(n))=0$, where $p(n)$, $L(n)$, and $W(n, x)$ are N-periodic in n, and $\nabla W(n, x)$ is asymptotically linear in x as $|x|\to\infty$. [ABSTRACT FROM AUTHOR]