Abstract
Consider the problem
{
−
Δ
u
+
f
(
|
x
|
λ
)
u
λ
2
=
|
u
|
4
N
−
2
u
in
B
1
,
u
=
0
on
∂
B
1
,
where
B
1
denotes the open unit ball in
R
N
,
N
⩾
3
and
λ
>
0
. Under some general assumptions on
f, we prove the existence or the non-existence of radial solutions. We consider also the case when
λ is determined.