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

Abstract

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.