Abstract
The aim of this paper is to establish the existence and global asymptotic behavior of a positive continuous solution for the following semilinear problem:
{
−
Δ
u
(
x
)
=
a
(
x
)
u
σ
(
x
)
,
x
∈
D
,
u
>
0
,
in
D
,
u
(
x
)
=
0
,
x
∈
∂
D
,
lim
|
x
|
→
∞
u
(
x
)
ln
|
x
|
=
0
,
where
σ
<
1
,
D
is an unbounded domain in
R
2
with a compact nonempty boundary
∂D
consisting of finitely many Jordan curves. As main tools, we use Kato class, Karamata regular variation theory and the Schauder fixed point theorem.