Electron. J. Diff. Equ., Vol. 2012 (2012), No. 79, pp. 1-20.

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

Elhoussine Azroul, Hicham Redwane, Chihab Yazough

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.

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Elhoussine Azroul
University of Fez, Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
B.P. 1796 Atlas Fez, Morocco
email: azroul_elhoussine@yahoo.fr
Hicham Redwane
Faculté des Sciences Juridiques, Economiques et Sociales
University Hassan 1
B.P. 784, Settat, Morocco
email: redwane_hicham@yahoo.fr
Chihab Yazough
University of Fez, Faculty of Sciences Dhar El Mahraz
Laboratory LAMA, Department of Mathematics
B.P. 1796 Atlas Fez, Morocco
email: chihabyazough@gmail.com

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