<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2020-0018_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mo>-</mo><mi>d</mi><mi>i</mi><mi>v</mi><mi> </mi><mi> </mi><mi>a</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>b</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><mi>H</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math><tex-math>- div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right),</tex-math></alternatives></disp-formula>where Ω is a bounded smooth domain of 𝕉<italic>N</italic>.</abstract>

In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation-div  a(x,u,∇u)=b(x)|u|p-2u+λH(x,u,∇u),- div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right),where Ω is a bounded smooth domain of 𝕉N.

Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

Moroccan Journal of Pure and Applied Analysis

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

In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the...

Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

Published Online: Oct 02, 2020

Page range: 231 - 242

Received: May 24, 2020

Accepted: Aug 20, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0018

Keywords
Weak solution, Neumann boundary condition, Berkovits topological degree, Sobolev spaces

© 2020 Adil Abbassi et al., published by Sciendo

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

Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

Published Online: Oct 02, 2020

Page range: 231 - 242

Received: May 24, 2020

Accepted: Aug 20, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0018

KeywordsWeak solution, Neumann boundary condition, Berkovits topological degree, Sobolev spaces

© 2020 Adil Abbassi et al., published by Sciendo

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

Keywords
Weak solution, Neumann boundary condition, Berkovits topological degree, Sobolev spaces