Symmetry of Positive Solutions for Fully Nonlinear Nonlocal Systems
In this paper, we consider the nonlinear systems involving fully nonlinear nonlocal operators { F α ( u ( x ) ) = v p ( x ) + k 1 ( x ) u r ( x ) , x ∈ ℝ N , G β ( v ( x ) ) = u q ( x ) + k 2 ( x ) v s ( x ) , x ∈ ℝ N and { F α ( u ( x ) ) = v p ( x ) | x | a + u r ( x ) | x | b , x ∈ ℝ N \ { 0 } ,...
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| Published in | Frontiers of Mathematics Vol. 19; no. 2; pp. 225 - 249 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Summary: | In this paper, we consider the nonlinear systems involving fully nonlinear nonlocal operators
{
F
α
(
u
(
x
)
)
=
v
p
(
x
)
+
k
1
(
x
)
u
r
(
x
)
,
x
∈
ℝ
N
,
G
β
(
v
(
x
)
)
=
u
q
(
x
)
+
k
2
(
x
)
v
s
(
x
)
,
x
∈
ℝ
N
and
{
F
α
(
u
(
x
)
)
=
v
p
(
x
)
|
x
|
a
+
u
r
(
x
)
|
x
|
b
,
x
∈
ℝ
N
\
{
0
}
,
G
β
(
v
(
x
)
)
=
u
q
(
x
)
|
x
|
c
+
v
s
(
x
)
|
x
|
d
,
x
∈
ℝ
N
\
{
0
}
,
where
k
i
(
x
) ≥ 0,
i
= 1, 2, 0 <
α
,
β
< 2,
p
,
q
,
r
,
s
> 1,
a
,
b
,
c
,
d
> 0. By proving a narrow region principle and other key ingredients for the above systems and extending the direct method of moving planes for the fractional
p
-Laplacian, we derive the radial symmetry of positive solutions about the origin. During these processes, we estimate the local lower bound of the solutions by constructing sub-solutions. |
|---|---|
| ISSN: | 2731-8648 1673-3452 2731-8656 1673-3576 |
| DOI: | 10.1007/s11464-021-0377-z |