PERIODIC SOLUTIONS OF SECOND ORDER LAGRANGIAN DIFFERENCE SYSTEMS WITH BOUNDED OR SINGULAR φ-LAPLACIAN AND PERIODIC POTENTIAL

T-periodic solutions of systems of difference equations of the form Delta phi[Delta q(n-1)] = del qF[n, q(n)] + h(n) (n is an element of Z) where phi = del Phi, with Phi strictly convex, is a homeomorphism of R-N onto the ball B-a subset of R-N, or a homeomorphism of the ball B-a subset of R-N onto R-N, are considered when F (n, u) is periodic in the u(j). The approach is variational.