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

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






-
d
i
v
 
 
a

(

x
,
u
,
∇
u

)

=
b

(
x
)





|
u
|




p
-
2


u
+
λ
H

(

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

.