In this work we examine the existence of positive classical solutions of
{
−
Δ
u
+
u
=
|
x
|
α
u
p
−
1
a
m
p
;
in
B
1
,
u
>
0
a
m
p
;
in
B
1
,
∂
ν
u
=
0
a
m
p
;
on
∂
B
1
,
\begin{equation*} \begin {cases} -\Delta u +u = |x|^\alpha u^{p-1} & \text { in } B_1, \\ u>0 & \text { in } B_1, \\ \partial _\nu u= 0 & \text { on } \partial B_1, \end{cases} \end{equation*}
where
p
>
1
p>1
,
α
>
0
\alpha >0
and
B
1
B_1
is the unit ball in
R
N
{\mathbb {R}}^N
where
N
≥
4
N \ge 4
and is even. Of particular interest is the existence of nonradial position classical solutions. We show that under suitable conditions on
p
,
α
p,\alpha
and
N
N
there are positive classical nonradial solutions. Our approach is to utilize a variational approach on suitable convex cones.