2002-Fez conference on Partial Differental Equations,
Electron. J. Diff. Eqns., Conf. 09, 2002, pp. 25-39.

Strongly nonlinear degenerated elliptic unilateral problems via convergence of truncations

Youssef Akdim, Elhoussine Azroul & Abdelmoujib Benkirane

Abstract:
We prove an existence theorem for a strongly nonlinear degenerated elliptic inequalities involving nonlinear operators of the form $Au+g(x,u,\nabla u)$. Here $A$ is a Leray-Lions operator, $g(x,s,\xi)$ is a lower order term satisfying some natural growth with respect to $|\nabla u|$. There is no growth restrictions with respect to $|u|$, only a sign condition. Under the assumption that the second term belongs to $W^{-1,p'}(\Omega,w^*)$, we obtain the main result via strong convergence of truncations.

Published December 28, 2002.
Subject classfications: 35J15, 35J70, 35J85.
Key words: Weighted Sobolev spaces, Hardy inequality, variational ineqality, strongly nonlinear degenerated elliptic operators, truncations.

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Youssef Akdim
Departement de Mathematiques et Informatique,
Faculte des Sciences Dhar-Mahraz,
B.P. 1796 Atlas, Fes, Maroc.
e-mail: y.akdim1@caramail.com
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

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