<abstract xmlns="http://www.w3.org/1999/xhtml">The aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2021-0006_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mi>A</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi></mrow></mtd><mtd><mrow><mi>i</mi><mi>n</mi></mrow></mtd><mtd><mi>Ω</mi></mtd></mtr><mtr><mtd><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></mtd><mtd><mrow><mi>o</mi><mi>n</mi></mrow></mtd><mtd><mrow><mo>∂</mo><mi>Ω</mi></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math><tex-math>\left\{ {\matrix{{A\left( u \right) = f} \hfill &amp; {in} \hfill &amp; \Omega \hfill \cr {u = 0} \hfill &amp; {on} \hfill &amp; {\partial \Omega } \hfill \cr } } \right.</tex-math></alternatives></disp-formula>where <italic>A</italic>(<italic>u</italic>) = −div<italic>a</italic>(<italic>x</italic>, <italic>u</italic>, ∇<italic>u</italic>) is a Leray-Lions operator and <italic>f</italic> ∈ <italic>W−1,p′</italic>(.)(Ω) with <italic>p</italic>(<italic>x</italic>) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.</abstract>

The aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form{A(u)=finΩu=0on∂Ω\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.

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

Department of Mathematics, Laboratory LAMA, Faculty of Sciences Dhar El Mahraz

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form{A(u)=finΩu=0on∂Ω\left\{ {\matrix{{A\left( u...

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

Publié en ligne: 22 nov. 2020

Pages: 50 - 65

Reçu: 26 avr. 2020

Accepté: 30 oct. 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0006

Mots clés
Nonlinear elliptic problem, Sobolev spaces with variable exponent, Topological degree, Normalising maps

© 2020 Mustapha Ait Hammou et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Publié en ligne: 22 nov. 2020

Pages: 50 - 65

Reçu: 26 avr. 2020

Accepté: 30 oct. 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0006

Mots clésNonlinear elliptic problem, Sobolev spaces with variable exponent, Topological degree, Normalising maps

© 2020 Mustapha Ait Hammou et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Nonlinear elliptic problem, Sobolev spaces with variable exponent, Topological degree, Normalising maps