Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces

Ouaarabi, Mohamed El; Abbassi, Adil; Allalou, Chakir

doi:10.1007/s41808-021-00102-3

Cited by 21 publications

(4 citation statements)

References 12 publications

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“…(Ω). For convenience, we only recall some basic facts with will be used later, we refer to [12,18,22,25,23,24] for more details.…”

Section: Preliminariesmentioning

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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“…(Ω). For convenience, we only recall some basic facts with will be used later, we refer to [12,18,22,25,23,24] for more details.…”

Section: Preliminariesmentioning

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.

Self Cite

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“…Furthermore, equipped by the norm (2.2), W 1,p (Ω, ω) and W 1,p 0 (Ω, ω) are separable and reflevixe Banach spaces. For more details on weighted Sobolev spaces W 1,p (Ω, ω), we propose to the reader [9,16,17,18,19].…”

Section: The Weighted Sobolev Spacesmentioning

confidence: 99%

Existence of Weak Solutions to a Class of Nonlinear Degenerate Parabolic Equations in Weighted Sobolev Space Mohamed El Ouaarabi, Chakir Allalou and Said Melliani

2023

Electronic Journal of Mathematical Analysis and Applications

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In this work, we prove the existence of a weak solutions for the initial boundary value problem associated with the nonlinear degenerate parabolic equationsWe will use the Topological degree theory for operators of the type T + S, where S is a bounded demicontinuous map of type (S + ) and T is a linear densely defined maximal monotone map with respect to a domain of T , and we study this problem in the space L p (0, T ; W 1,p 0 (Ω, ω)), where Ω is a bounded domain in R N (N ≥ 2), p ≥ 2 and ω is a vector of weight functions.

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“…Motivated by above, we study (1), on the one hand as a kind of generalisation of the previous work, and on the other hand, using another approach based on the topological degree theory for operators of the type L + S, where L is a linear densely defined maximal monotone map and S is a bounded demicontinuous map of type (S + ) with respect to a domain of L. For more information on the history of this theory, the reader should consult [1,2,3,6,7,9,16,17,19].…”

Section: Introductionmentioning

confidence: 99%

Existence of a weak solutions to a class of nonlinear parabolic problems via topological degree method

Ouaarabi

Allalou

Melliani

2023

GJOM

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In this paper, we study the existence of "weak solutions" for a class of nonlinear parabolic problems of the type ∂ u⁄∂ t - div Α (x, t, ∇ u) = Φ (x, t) + div B(x, t, u, ∇ u). Using Berkovits and Mustonen's topological degree theory, we demonstrate the existence of a weak solutions to the problems under consideration in the space Lp(0, T, W01, p(Ω)), where Ω is a bounded domain in RN, N ≥ 2 and p ≥ 2.

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Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces

Cited by 21 publications

References 12 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

Existence of Weak Solutions to a Class of Nonlinear Degenerate Parabolic Equations in Weighted Sobolev Space Mohamed El Ouaarabi, Chakir Allalou and Said Melliani

Existence of a weak solutions to a class of nonlinear parabolic problems via topological degree method

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