Affiliation:
1. Hubei Minzu University
Abstract
This paper is devoted to studying the existence of positive solutions of the problem:
(
∗
)
{
−
Δ
u
=
u
p
|
x
|
a
+
h
(
x
,
u
,
∇
u
)
,
in
Ω
,
u
=
0
,
on
∂
Ω
,
where
Ω
⊂
R
N
(
N
≥
3
)
is an open bounded smooth domain with boundary
∂
Ω
, and
1
<
p
<
N
−
a
N
−
2
,
0
<
a
<
2
. Under suitable conditions of
h
(
x
,
u
,
∇
u
)
, we get a priori estimates for the positive solutions of problem
(
∗
)
. By making use of these estimates and topological degree theory, we further obtain some existence results for the positive solutions of problem
(
∗
)
when
1
<
p
<
N
−
a
N
−
2
.