Existence of Entropy Solutions for Anisotropic Elliptic Nonlinear Problem in Weighted Sobolev Space

Abbassi, Adil; Allalou, Chakir; Kassidi, Abderrazak

doi:10.1007/978-3-030-62299-2_8

Cited by 8 publications

(6 citation statements)

References 8 publications

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“…Now, we give some results and properties from the theory of topological degree. The readers can find more information about the history of this theory in [1,2,6,16].…”

Section: A Review On the Topological Degree Theorymentioning

confidence: 99%

A p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-Like Operators With Dirichlet Boundary Condition

El Ouaarabi,

El Hammar,

Allalou

et al. 2024

Stud. Univ. Babes-Bolyai Math.

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This paper deals with a class of p(x)-Kirchhoff type problems involving the p(x)-Laplacian-like operators, arising from the capillarity phenomena, depending on two real parameters with Dirichlet boundary conditions. Using a topological degree for a class of demicontinuous operators of generalized (S+), we prove the existence of weak solutions of this problem. Our results extend and generalize several corresponding results from the existing literature. Keywords: p(x)-Kirchhoff type problems, p(x)-Laplacian-like operators, weak solutions, variable exponent Sobolev spaces.

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“…Now, we give some results and properties from the theory of topological degree. The readers can find more information about the history of this theory in [1,2,6,16].…”

Section: A Review On the Topological Degree Theorymentioning

confidence: 99%

A p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-Like Operators With Dirichlet Boundary Condition

El Ouaarabi,

El Hammar,

Allalou

et al. 2024

Stud. Univ. Babes-Bolyai Math.

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“…In this section we recall some fundamental definitions and theorems about topological degree theory which are useful for our aim, and we refer the reader to [1,2,15,24] for more details.…”

Section: Necessary Facts On the Topological Degreementioning

confidence: 99%

“…The following lemmas allow us to transform this discontinuous nonlinear elliptic problems (1) with Neumann boundary condition into a new one governed by a Hammerstein equation.…”

Section: ( Homotopy Invariance)mentioning

confidence: 99%

“…, p N with p i are real numbers, p i ≥ 2, we get the anisotropic − → p -Laplace operator, we refer to the recent paper by Figueiredo and Silva [22] have established the existence of a nonnegative solution for nonlinear anisotropic elliptic equations. Some related results can be found in [3,5]. This paper is organized as follows: In the next section, we recall some basic definitions and preliminary results.…”

Section: Introduction and Hypothesesmentioning

confidence: 99%

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A weak solution to a Kirkoff type problem with discontinuous nonlinearities

Kassidi,

Melliani,

Sabiry

et al. 2023

BUT_Series_III

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“…(Ω) and proving an existence result without sign condition on g. Recent studies on elliptic problems, Hardy potential and entropy theory can be found in several papers by Di Fazio, Hjiej, Ragusa, such as [7,10,19,25]. More information on degenerate nonlinear elliptic equations can be found in [1,2,3].…”

Section: Introductionmentioning

confidence: 99%

Existence Results in Weighted Sobolev Space for Quasilinear Degenerate P(z)−elliptic Problems With a Hardy Potential

Zineddaine,

Sabiry,

Melliani

et al. 2024

Mathematical Modelling and Analysis

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The objective of this work is to establish the existence of entropy solutions to degenerate nonlinear elliptic problems for $L^1$-data $f$ with a Hardy potential, in weighted Sobolev spaces with variable exponent, which are represented as follows \begin{gather*} -\text{div}\big(\Phi(z,v,\nabla v)\big)+g(z,v,\nabla v)=f+\rho\frac{\vert v \vert^{p(z)-2}v}{|v|^{p(z)}}, \end{gather*} where $-\text{div}(\Phi(z,v,\nabla v))$ is a Leray-Lions operator from $W_{0}^{1,p(z)}(\Omega,\omega)$ into its dual, $g(z,v,\nabla v)$ is a non-linearity term that only meets the growth condition, and $\rho>0$ is a constant.

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Existence of Entropy Solutions for Anisotropic Elliptic Nonlinear Problem in Weighted Sobolev Space

Cited by 8 publications

References 8 publications

A p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-Like Operators With Dirichlet Boundary Condition

A p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-Like Operators With Dirichlet Boundary Condition

A weak solution to a Kirkoff type problem with discontinuous nonlinearities

Existence Results in Weighted Sobolev Space for Quasilinear Degenerate P(z)−elliptic Problems With a Hardy Potential

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