Abstract and Applied Analysis
Volume 2006 (2006), Article ID 46867, 20 pages

Strongly nonlinear elliptic variational unilateral problems in Orlicz space

L. Aharouch, A. Benkirane, and M. Rhoudaf

Département de Mathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, Université Sidi Mohamed Ben Abdallah B.P. 1796, Atlas Fès, Morocco

Received 2 March 2005; Accepted 12 April 2005

Copyright © 2006 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 unilateral problem associated to the equations of the form Au+g(x,u,u)=f, where A is a Leray-Lions operator from its domain D(A)W01LM(Ω) into W1EM¯(Ω). On the nonlinear lower order term g(x,u,u), we assume that it is a Carathéodory function having natural growth with respect to |u|, and satisfies the sign condition. The right-hand side f belongs to W1EM¯(Ω).