Geodesic
Strongly Nonlinear Elliptic Unilateral Problems without Sign Condition and L1 Data
Journal of convex analysis, Tome 13 (2006) no. 1, pp. 135-149.

Voir la notice de l'article provenant de la source Heldermann Verlag

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 $L^1(\Omega)$.
Classification : 35J25, 35J60, 35J65
Mots-clés : Sobolev spaces, strongly nonlinear inequality, truncations, unilateral problems 
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     author = {L. Aharouch and Y. Akdim},
     title = {Strongly {Nonlinear} {Elliptic} {Unilateral} {Problems} without {Sign} {Condition} and {L\protect\textsuperscript{1}} {Data}},
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L. Aharouch; Y. Akdim. Strongly Nonlinear Elliptic Unilateral Problems without Sign Condition and L1 Data. Journal of convex analysis, Tome 13 (2006) no. 1, pp. 135-149. http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a8/