Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential

T-periodic solutions of systems of difierence equations of the form [q(n 1)] = rqF[n; q(n)] + h(n) (n 2 Z) where = r, with strictly convex, is a homeomorphism of RN onto the ball Ba RN, or a homeomorphism of the ball Ba RN onto RN, are considered when F(n; u) is periodic in the uj . The approach is variational