Extremal solutions for a class of unilateral problems

We apply a fixed point theorem for increasing operators in ordered Banach spaces to prove the existence of extremal (i.e. maximal or minimal) solutions for the variational inequality [Av, w - v] greater than or equal to integral(Omega) f(x, v)(w - v) dx where A is the p-Laplacian and f(x, u) = F(x, u, u) with F(x, u, v) being a function, non-decreasing in u and non-increasing in v.