Abstract

We will be concerned with the existence result of a degenerate elliptic unilateral problem of the form Au+H(x,u,∇u)=f, where A is a Leray-Lions operator from W1,p(Ω,w) into its dual. On the nonlinear lower-order term H(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 side f belongs to L1(Ω).