Abstract

We prove the existence of solutions of unilateral problems involving nonlinear operators of the form Au+H(x,u,∇u)=fAu + H(x, u, \nabla u) = f where AA is a Leray Lions operator from W01,p(Ω)W_0^{1, p}(\Omega) into its dual W−1,p′(Ω)W^{-1, p'}(\Omega) and H(x,u,∇u)H(x, u, \nabla u) is a nonlinearity which satisfies the following growth condition ∣H(x,s,ξ)∣≤γ(x)+g(s)∣ξ∣p|H(x, s, \xi)| \leq \gamma(x)+g(s) |\xi|^p with γ∈L1(Ω)\gamma\in L^1(\Omega) and g∈L1(R)g\in L^1({\mathbb R}), and without assuming any sign condition on H(x,s,ξ)H(x, s, \xi). The right hand side ff belongs to L1(Ω)L^1(\Omega).

Author information

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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

Keywords

  • Sobolev spaces
  • strongly nonlinear inequality
  • truncations
  • unilateral problems

Mathematics Subject Classification

35J25; 35J60, 35J65

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Suggested citation

L. Aharouch, Y. Akdim. “Strongly Nonlinear Elliptic Unilateral Problems without Sign Condition and L^1 Data.” Journal of Convex Analysis 13 (2006), No. 1, 135–149. https://doi.org/10.68381/jca13009

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.