In this paper, we deal with the second order discrete Hamiltonian system Delta[p(n) Delta u (n - 1)]- L(n)u(n) + Delta W(n; u ( n)) = 0, where L : Z -> R (NxN) is positive de fi nite for su ffi ciently large vertical bar n vertical bar epsilon Z and W(n; x) is inde fi nite sign. By using critical point theory, we establish some new criteria to guarantee that the above system has in fi nitely many nontrivial homoclinic solutions under the assumption that W(n; x) is asymptotically quadratic and supquadratic, respectively. Our r...
