Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 79, pp. 1-20.

Title:  Strongly nonlinear nonhomogeneous elliptic unilateral problems
        with L^1 data and no sign conditions

Authors: Elhoussine Azroul (Univ. of Fez, Atlas Fez, Morocco)
         Hicham Redwane (Univ. Hassan 1, Settat, Morocco)
	 Chihab Yazough (Univ. of Fez, Atlas Fez, Morocco)

Abstract:
 In this article, we prove the existence of solutions to unilateral
 problems involving nonlinear operators of the form:
 $$ Au+H(x,u,\nabla u)=f $$
 where $A$ is a Leray Lions operator  from
 $W_0^{1,p(x)}(\Omega)$ into its dual $W^{-1,p'(x)}(\Omega)$ and
 $H(x,s,\xi)$ is the nonlinear term satisfying some growth condition
 but no sign condition. The right hand side $f$ belong to $L^1(\Omega)$.

Submitted September 19, 2011. Published May 15, 2012.
Math Subject Classifications: 35J60.
Key Words: Entropy solutions; variable exponent; unilateral problem.