Barrier solutions of elliptic variational inequalities

We consider elliptic variational inequalities in a bounded domain Ω⊂RNΩ⊂RN of the formu∈K:〈Au+λ|u|p−2u+F(u),v−u〉≥〈h,v−u〉,∀v∈K, where AA is a second order quasilinear elliptic operator of divergence type, FF is the operator generated by lower order terms, and KK is a closed convex subset of the Sobolev space W1,p(Ω)W1,p(Ω), 1