Abstract
We consider the following singular semilinear problem
{
Δ
u
(
x
)
+
p
(
x
)
u
γ
=
0
,
x
∈
D
(
in the distributional sense
)
,
u
>
0
,
in
D
,
lim
|
x
|
→
0
|
x
|
n
−
2
u
(
x
)
=
0
,
lim
|
x
|
→
∞
u
(
x
)
=
0
,
where
γ
<
1
,
D
=
R
n
∖
{
0
}
(
n
≥
3
) and
p
is a positive continuous function in
D
, which may be singular at
x
=
0
. Under sufficient conditions for the weighted function
p
(
x
)
, we prove the existence of a positive continuous solution on
D
, which could blow-up at the origin. The global asymptotic behavior of this solution is also obtained.