Nonlinear elliptic unilateral problem existence of solutions

We prove existence of a solution of the elliptic unilateral problem. The nonlinear operator is of the form A(u) + F(x, u, Du) in an unbounded domain Omega of R-n. The operator is defined from the space W-0(1,p)(Omega) into the space W--1,W-P'(Omega). F has growth of order p with respect to variable Du satisfying the sign condition. The obstacle is a measurable function with variable in (R) over bar. A and F satisfy Caratheodory conditions. The case p < 2 could be handled under some conditions on coefficients to obtain a priori estimates. (see [3], [5] & [10]). The last section gives an idea about numerical approach of the unilateral problem.