Abstract and Applied Analysis
Volume 2005 (2005), Issue 1, Pages 11-31

Quasilinear degenerate elliptic unilateral problems

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

Département deMathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, BP 1796 Atlas, Fès, Morocco

Received 20 February 2004

Copyright © 2005 L. Aharouch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).