Abstract
Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system
(
−
Δ
|
D
)
α
/
2
u
+
p
(
x
)
u
σ
v
r
=
0
,
(
−
Δ
|
D
)
α
/
2
v
+
q
(
x
)
u
s
v
β
=
0
in a bounded
C
1
,
1
-domain
D
in
ℝ
n
(
n
≥
3
)
, subject to some Dirichlet conditions, where
0
<
α
<
2
,
σ
,
β
≥
1
,
s
,
r
≥
0.
The potential functions
p
,
q
are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions
K
α
(
D
)
.