Electron. J. Diff. Eqns., Vol. 2001(2001), No. 71, pp. 1-19.

Existence of solutions for quasilinear degenerate elliptic equations

Y. Akdim, E. Azroul, & A. Benkirane

Abstract:
In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form $A(u)+g(x,u,\nabla u)=h$, where $A$ is a Leray-Lions operator from $W_0^{1,p}(\Omega,w)$ to its dual. On the nonlinear term $g(x,s,\xi)$, we assume growth conditions on $\xi$, not on $s$, and a sign condition on $s$.

Submitted October 16, 2001. Published November 26, 2001.
Math Subject Classifications: 35J15, 35J20, 35J70.
Key Words: Weighted Sobolev spaces, Hardy inequality, Quasilinear degenerate elliptic operators.

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