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〉 ≥ R Ω f(x, v)(w − v) dx where A is the pLaplacian 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.