Neumann Problem with a Nonlinear p(x)-Elliptic Equation Solved by Topological Degree Methods

Soukaina Yacini; Abderrazak Kassidi; Chakir Allalou; Khalid Hilal

doi:10.2478/tmmp-2025-0021

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Neumann Problem with a Nonlinear p(x)-Elliptic Equation Solved by Topological Degree Methods

Tatra Mountains Mathematical Publications

Volume 90 (2025): Issue 2 (December 2025)

By: Soukaina Yacini, Abderrazak Kassidi, Chakir Allalou and Khalid Hilal

Open Access

|Dec 2025

Abstract

In this paper, we prove the existence of weak solutions to Neumann boundary value problems for a nonlinear p(x)-elliptic equation of the form $- div a (x, u, \nabla u) = b (x) {| u |}^{p (x) - 2} u + λ H (x, u, \nabla u) .$ - {\rm{div}}\,a(x,u,\nabla u) = b\left( x \right){\left| u \right|^{p\left( x \right) - 2}}u + \lambda H\left( {x,u,\,\nabla u} \right). We established the existence result by using the topological degree introduced by Berkovits.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0021 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 15 - 34

Submitted on: Jan 21, 2022

Accepted on: Aug 8, 2025

Published on: Dec 18, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

weak solution,

Neumann boundary condition,

topological degree theory,

Berkovits topological degree

Related subjects:

Mathematics,

General mathematics

© 2025 Soukaina Yacini, Abderrazak Kassidi, Chakir Allalou, Khalid Hilal, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 90 (2025): Issue 2 (December 2025)