2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 73-81.

Leray Lions degenerated problem with general growth condition

Youssef Akdim, Abdelmoujib Benkirane, Mohamed Rhoudaf

Abstract:
In this paper, we study the existence of solutions for the nonlinear degenerated elliptic problem
$$ -\operatorname{div}(a(x,u,\nabla u)) = F\quad \text{in } \Omega, $$
where $\Omega$ is a bounded domain of $\mathbb{R}^N$, $N \geq 2$, $a:\Omega\times\mathbb{R}\times\mathbb{R}^N\to\mathbb{R}^N $ is a Caratheodory function satisfying the coercivity condition, but they verify the general growth condition and only the large monotonicity. The second term $F$ belongs to $W^{-1, p'}(\Omega, w^*)$.

Published September 20, 2006.
Math Subject Classifications: 35J15, 35J70, 35J85.
Key Words: Weighted Sobolev spaces; truncations; $L^1$-version of Minty's lemma; Hardy inequality.

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Youssef Akdim
Département de Mathématiques et Informatique
Faculté des Sciences Dhar-Mahraz
B. P. 1796 Atlas Fès, Maroc
email: akdimyoussef@yahoo.fr
Abdelmoujib Benkirane
Département de Mathématiques et Informatique
Faculté des Sciences Dhar-Mahraz
B. P. 1796 Atlas Fès, Maroc
email: abenkirane@fsdmfes.ac.ma
Mohamed Rhoudaf
Département de Mathématiques et Informatique
Faculté des Sciences Dhar-Mahraz
B. P. 1796 Atlas Fès, Maroc
email: rhoudaf_mohamed@yahoo.fr

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