Journal of Convex Analysis 13 (2006), No. 1, 135--149
Copyright Heldermann Verlag 2006
Strongly Nonlinear Elliptic Unilateral Problems without Sign Condition and L1 Data
Lahsen Aharouch
Dép. de Mathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, B. P. 1796 Atlas Fès, Morocco
l_aharouch@yahoo.fr
Youssef Akdim
Dép. de Mathématiques et Informatique, Faculté des Sciences Dhar-Mahraz, B. P. 1796 Atlas Fès, Morocco
akdimyoussef@yahoo.fr
[Abstract-pdf]
We prove the existence of solutions of unilateral problems involving nonlinear operators of the form $$Au + H(x, u, \nabla u) = f $$ where $A$ is a Leray Lions operator from $W_0^{1, p}(\Omega)$ into its dual $W^{-1, p'}(\Omega)$ and $H(x, u, \nabla u)$ is a nonlinearity which satisfies the following growth condition $|H(x, s, \xi)| \leq \gamma(x)+g(s) |\xi|^p$ with $\gamma\in L^1(\Omega)$ and $g\in L^1({\mathbb R})$, and without assuming any sign condition on $H(x, s, \xi)$. The right hand side $f$ belongs to $L^1(\Omega)$.
Keywords: Sobolev spaces, strongly nonlinear inequality, truncations, unilateral problems.
MSC: 35J25; 35J60, 35J65
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