Journal article
Existence and symmetry of positive solutions of an integral equation system
Mathematical and computer modelling, Vol.52(5), pp.892-901
2010
DOI: 10.1016/j.mcm.2010.05.020
Abstract
In this paper, we investigate positive solutions of the following integral equation system in
R
n
:
{
u
(
x
)
=
∫
R
n
∣
x
−
y
∣
α
−
n
v
(
y
)
p
d
y
,
v
(
x
)
=
∫
R
n
∣
x
−
y
∣
β
−
n
u
(
y
)
q
d
y
,
where
p
,
q
>
1
,
0
<
α
,
β
<
n
. With the method of moving spheres, we show the existence and the exact form of its solution in the case
p
≤
(
n
+
α
)
/
(
n
−
β
)
,
q
≤
(
n
+
β
)
/
(
n
−
α
)
;
and with the method of moving planes, we prove the symmetry and monotonicity of its solution in the case
1
p
+
1
+
1
q
+
1
=
n
−
α
2
n
+
β
−
α
+
n
−
β
2
n
+
α
−
β
.
Details
- Title: Subtitle
- Existence and symmetry of positive solutions of an integral equation system
- Creators
- Xiaotao Huang - College of Science, Xi’an Jiaotong University, Xi’an 710049, PR ChinaDongsheng Li - College of Science, Xi’an Jiaotong University, Xi’an 710049, PR ChinaLihe Wang - College of Science, Xi’an Jiaotong University, Xi’an 710049, PR China
- Resource Type
- Journal article
- Publication Details
- Mathematical and computer modelling, Vol.52(5), pp.892-901
- DOI
- 10.1016/j.mcm.2010.05.020
- ISSN
- 0895-7177
- eISSN
- 1872-9479
- Publisher
- Elsevier Ltd
- Grant note
- DOI: 10.13039/501100001809, name: NSFC, award: 10771166; name: NSF, award: DMS-0701392
- Language
- English
- Date published
- 2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984083806702771
Metrics
31 Record Views