2002-Fez conference on Partial Differental Equations,
Electron. J. Diff. Eqns., Conf. 09, 2002, pp. 49-64.

Strongly nonlinear degenerated unilateral problems with $L^1$ data

Elhoussine Azroul, Abdelmoujib Benkirane & Ouidad Filali

Abstract:
In this paper, we study the existence of solutions for strongly nonlinear degenerated unilateral problems associated to nonlinear operators of the form $Au+g(x,u,\nabla u)$. Here $A$ is a Leray-Lions operator acting from $W_0^{1,p}(\Omega,w)$ into its dual, while $g(x,s,\xi)$ is a nonlinear term which has a growth condition with respect to $\xi$ and no growth condition with respect to $s$, the second term belongs to $L^1(\Omega )$.

Published December 28, 2002.
Subject classfications: 35J15, 35J70, 35J85.
Key words: Weighted Sobolev spaces, Hardy inequality, quasilinear degenerated elliptic operators.

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Elhoussine Azroul
Departement de Mathematiques et Informatique,
Faculte des Sciences Dhar-Mahraz,
B.P. 1796 Atlas, Fes, Maroc.
e-mail: elazroul@caramail.com
Abdelmoujib Benkirane
Departement de Mathematiques et Informatique,
Faculte des Sciences Dhar-Mahraz,
B.P. 1796 Atlas, Fes, Maroc.
e-mail: abdelmoujib@iam.net.ma
Ouidad Filali
Departement de Mathematiques et Informatique,
Faculte des Sciences Dhar-Mahraz,
B.P. 1796 Atlas, Fes, Maroc.
e-mail: ouidadf@hotmail.com

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