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Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent Cover

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Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent

Moroccan Journal of Pure and Applied Analysis

Volume 7 (2021): Issue 1 (January 2021)

By: Mustapha Ait Hammou and Elhoussine Azroul

Open Access

|Nov 2020

Abstract

The aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form

${\begin{matrix} A (u) = f & i n & Ω \\ u = 0 & o n & \partial Ω \end{matrix}$ \left\{ {\matrix{{A\left( u \right) = f} \hfill & {in} \hfill & \Omega \hfill \cr {u = 0} \hfill & {on} \hfill & {\partial \Omega } \hfill \cr } } \right.

where A(u) = −diva(x, u, ∇u) is a Leray-Lions operator and f ∈ W^−1,p′^(.)(Ω) with p(x) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.

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Articles in this issue

DOI: https://doi.org/10.2478/mjpaa-2021-0006 | Journal eISSN: 2351-8227

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Language: English

Page range: 50 - 65

Submitted on: Apr 26, 2020

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Accepted on: Oct 30, 2020

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Published on: Nov 22, 2020

Published by: Sciendo

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Nonlinear elliptic problem,

Sobolev spaces with variable exponent,

Topological degree,

Normalising maps

Related subjects:

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics

© 2020 Mustapha Ait Hammou, Elhoussine Azroul, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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