Quasilinear degenerate elliptic unilateral problems

Abstract

We will be concerned with the existence result of a degenerate elliptic unilateral problem of the formAu+H(x,u,∇u)=f, whereAis a Leray-Lions operator fromW1,p(Ω,w)into its dual. On the nonlinear lower-order termH(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to|∇u|, but without assuming the sign condition. The right-hand sidefbelongs toL1(Ω).