Electronic Journal of Differential Equations,
Conference 09 (2002), pp. 49-64.

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

Authors: Elhoussine Azroul (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
  Abdelmoujib Benkirane (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
  Ouidad Filali (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)

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.
Math Subject Classifications: 35J15, 35J70, 35J85.
Key Words: Weighted Sobolev spaces; Hardy inequality;
  quasilinear degenerated elliptic operators.