Singular discrete second order BVPs with p-Laplacian

We study singular discrete boundary value problems with mixed boundary conditions and with the p-Laplacian of the form Delta(phi(p)(Delta u(t - 1))) + f(t, u(t), Delta u(t - 1)) = 0 t is an element of [1, T + 1] Delta u(0) = u(T + 2) = 0 where [1, T + 1] = {1, 2,..., T + 1}, T is an element of N, phi(p)(y) = vertical bar y vertical bar(P-2)y, p > 1. We assume that f is continuous on [1,T + 1] X (0, infinity) X R and f(t,x,y) has a singularity at x = 0. We prove the existence of a positive solution by means of lower and upper functions method, Brouwer fixed point theorem and by a convergence of approximate regular problems.