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

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 - d i v a ( x , u , ∇ u ) = b ( x ) | u | p - 2 u + λ H ( x , u , ∇ u ) , - div\,\,a( {x,u,∇ u} ) = b( x ){| u |p - 2}u + λ H( {x,u,∇ u} ), where Ω is a bounded smooth domain of 𝕉 N .