Abstract
This paper is devoted to the study the following nonlinear fractional elliptic system:
{
(
−
Δ
)
α
2
u
(
x
)
=
h
1
(
x
,
u
(
x
)
,
v
(
x
)
)
,
(
−
Δ
)
β
2
v
(
x
)
=
h
2
(
x
,
u
(
x
)
,
v
(
x
)
)
,
where
0
α
,
β
2
,
n
≥
2
and
h
1
,
h
2
satisfy suitable assumptions. We employ the method of scaling spheres to establish the nonexistence of nonnegative solutions for this fractional elliptic system in the entire space
R
n
. Furthermore, we show that analogous results can be extended for higher order fractional problems.