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On a necessary condition in the calculus of variations in Orlicz-Sobolev spaces

Elhoussine Azroul; Abdelmoujib Benkirane — 2001

Mathematica Slovaca

Existence of solutions of strongly nonlinear elliptic equations in R.

Abdelmoujib Benkirane; M. Kbiri Alaoui — 2001

Revista Matemática Complutense

The paper is dedicated to the existence of local solutions of strongly nonlinear equations in R and the Orlicz spaces framework is used.

Existence results for quasilinear degenerated equations via strong convergence of truncations.

Youssef Akdim; Elhoussine Azroul; Abdelmoujib Benkirane — 2004

Revista Matemática Complutense

In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x,u,∇u) = f, where A is a Leray-Lions operator from W (Ω,ω) into its dual, while g(x,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong either to W(Ω,ω*) or to L(Ω).

Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems

Youssef Akdim; Elhoussine Azroul; Abdelmoujib Benkirane — 2003

Annales mathématiques Blaise Pascal

An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form $A u + g (x, u, \nabla u)$ , where $A$ is a Leray-Lions operator from $W_{0}^{1, p} (Ω, w)$ into its dual, while $g (x, s, ξ)$ is a nonlinear term which has a growth condition with respect to $ξ$ and no growth with respect to $s$ , but it satisfies a sign condition on $s$ , the second term belongs to $W^{- 1, p^{'}} (Ω, w^{*})$ .

Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces

Azeddine Aissaoui Fqayeh; Abdelmoujib Benkirane; Mostafa El Moumni — 2014

Applicationes Mathematicae

We discuss the existence of entropy solution for the strongly nonlinear unilateral parabolic inequalities associated to the nonlinear parabolic equations ∂u/∂t - div(a(x,t,u,∇u) + Φ(u)) + g(u)M(|∇u|) = μ in Q, in the framework of Orlicz-Sobolev spaces without any restriction on the N-function of the Orlicz spaces, where -div(a(x,t,u,∇u)) is a Leray-Lions operator and $Φ \in C ⁰ (ℝ, ℝ^{N})$ . The function g(u)M(|∇u|) is a nonlinear lower order term with natural growth with respect to |∇u|, without satisfying the sign...

An existence theorem for a strongly nonlinear elliptic problem in Musielak-Orlicz spaces

Abdelmoujib Benkirane; Fatimazahra Blali; Mohamed Sidi El Vally — 2014

Applicationes Mathematicae

We prove an existence result for some class of strongly nonlinear elliptic problems in the Musielak-Orlicz spaces $W ¹ L_{φ} (Ω)$ , under the assumption that the conjugate function of φ satisfies the Δ₂-condition.

Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data

M.S.B. Elemine Vall; A. Ahmed; A. Touzani; Abdelmoujib Benkirane — 2020

Archivum Mathematicum

We prove an existence result of entropy solutions for a class of strongly nonlinear parabolic problems in Musielak-Sobolev spaces, without using the sign condition on the nonlinearities and with measure data.

Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form

Mohamed Saad Bouh Elemine Vall; Ahmed Ahmed; Abdelfattah Touzani; Abdelmoujib Benkirane — 2018

Mathematica Bohemica

We prove the existence of solutions to nonlinear parabolic problems of the following type: $\{\begin{matrix} \frac{\partial b (u)}{\partial t} + A (u) = f + div (Θ (x; t; u)) & in Q, \\ u (x; t) = 0 & on \partial Ω \times [0; T], \\ b (u) (t = 0) = b (u_{0}) & on Ω, \end{matrix}$ where $b : ℝ \to ℝ$ is a strictly increasing function of class $𝒞^{1}$ , the term $A (u) = - div (a (x, t, u, \nabla u))$ is an operator of Leray-Lions type which satisfies the classical Leray-Lions assumptions of Musielak type, $Θ : Ω \times [0; T] \times ℝ \to ℝ$ is a Carathéodory, noncoercive function which satisfies the following condition: ${sup}_{| s | \leq k} | Θ (\cdot, \cdot, s) | \in E_{ψ} (Q)$ for all $k > 0$ , where $ψ$ is the Musielak complementary function of $Θ$ , and the second term $f$ belongs to $L^{1} (Q)$ .

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Currently displaying 1 – 12 of 12

On a necessary condition in the calculus of variations in Orlicz-Sobolev spaces

Existence of solutions of strongly nonlinear elliptic equations in R.

Existence results for quasilinear degenerated equations via strong convergence of truncations.

Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems

Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces

An existence theorem for a strongly nonlinear elliptic problem in Musielak-Orlicz spaces

Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data

Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form

On the $L^{\infty}$ -regularity of solutions of nonlinear elliptic equations in Orlicz spaces.

Leray Lions degenerated problem with general growth condition.

Strongly nonlinear degenerated unilateral problems with $L^{1}$ data.

Strongly nonlinear degenerated elliptic unilateral problems via convergence of truncations.