In this paper, we investigate the second order self-adjoint discrete Hamiltonian system Δ[p(n)Δu(n - 1)] - L(n)u(n) + λa(n)∇G(u(n)) + µb(n)∇F(u(n)) = 0, where p, L: Z→RN×N are both positive definite for all n ε Z, and no symmetric condition on G and F is needed. We establish two new criteria to guarantee that the above system has at least two nontrivial homoclinic solutions or infinitely many homoclinic solutions ...
