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 $Au+g(x,u,\nabla u)$, where $A$ is a Leray-Lions operator from $W_0^{1,p}(\Omega ,w)$ into its dual, while $g(x,s,\xi )$ is a nonlinear term which has a growth condition with respect to $\xi$ and no growth with respect to $s$, but it satisfies a sign condition on $s$, the second term belongs to $W^{-1,p^{\prime }}(\Omega ,w^{*})$.