Quasilinear degenerate elliptic unilateral problems. (English) Zbl 1236.35081

Aharouch, L.; Akdim, Y.; Azroul, E.

Abstr. Appl. Anal. 2005, No. 1, 11-31 (2005).

Summary: We are concerned with the existence result of a degenerate elliptic unilateral problem of the form \(Au + H(x, u, \nabla u) = f\) , where \(A\) is a Leray-Lions operator from \(W^{1,p}(\Omega, w)\) into its dual. On the nonlinear lower-order term \(H(x,u,\nabla u)\), we assume that it is a Carathéodory function having natural growth with respect to \(|\nabla u|\), but without assuming the sign condition. The right-hand side \(f\) belongs to \(L^{1}(\Omega)\).

MSC:

35J87	Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
35J60	Nonlinear elliptic equations
35J70	Degenerate elliptic equations