Strongly nonlinear elliptic variational unilateral problems in Orlicz space

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

doi:https://doi.org/10.1155/AAA/2006/46867

Abstract and Applied Analysis

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Volume 2006 | Article ID 046867 | https://doi.org/10.1155/AAA/2006/46867

Strongly nonlinear elliptic variational unilateral problems in Orlicz space

L. Aharouch,¹A. Benkirane,¹and M. Rhoudaf¹

Received02 Mar 2005

Accepted12 Apr 2005

Published21 Feb 2006

Abstract

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 W−1EM¯(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 W−1EM¯(Ω).

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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.

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