2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 73-81. 

Title: Leray Lions degenerated problem with general 
       growth condition

Authors: Youssef Akdim  (Faculte des Sciences Dhar-Mahraz, Maroc)
         Abdelmoujib Benkirane (Faculte des Sciences Dhar-Mahraz, Maroc)
	 Mohamed Rhoudaf (Faculte des Sciences Dhar-Mahraz, Maroc)
 
Abstract: 
 In this paper, we study the existence of solutions for the
 nonlinear degenerated elliptic problem
 $$
 -{\mathop{\rm div}}(a(x,u,\nabla u)) = F\quad \mbox{in }  \Omega,
 $$
 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.