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

Yacini, Soukaina; Kassidi, Abderrazak; Allalou, Chakir; Hilal, Khalid

doi:10.2478/tmmp-2025-0021

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

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