Electronic Journal of Differential Equations,
Conference 09 (2002), pp. 25-39.

Title: Strongly nonlinear degenerated elliptic unilateral problems
  via convergence of truncations

Authors: Youssef Akdim (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
  Elhoussine Azroul (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
  Abdelmoujib Benkirane (Faculte des Sciences Dhar-Mahraz, Fes, Maroc)
 
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.
Math Subject Classifications: 35J15, 35J70, 35J85.
Key Words: Weighted Sobolev spaces; Hardy inequality; 
  variational ineqality; strongly nonlinear degenerated elliptic operators; truncations.