Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems

An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form Au+g(x, u, ⊇u), where A is a Leray-Lions operator from W 1,p 0 (Ω, w) into its dual, while g(x, s, ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s, the second term belongs to W -1,p' (Ω,w*).