Abstract
Abstract
We study the asymptotic behavior of positive radial solutions for quasilinear elliptic systems that have the form
Δ
p
u
=
c
1
|
x
|
m
1
⋅
g
1
v
⋅
|
∇
u
|
α
in
R
n
,
Δ
p
v
=
c
2
|
x
|
m
2
⋅
g
2
v
⋅
g
3
|
∇
u
|
in
R
n
,
where
Δ
p
denotes the p-Laplace operator, p > 1,
n
⩾
2
,
c
1
,
c
2
>
0
and
m
1
,
m
2
,
α
⩾
0
. For a general class of functions gj
which grow polynomially, we show that every non-constant positive radial solution (u, v) asymptotically approaches
(
u
0
,
v
0
)
=
(
C
λ
|
x
|
λ
,
C
μ
|
x
|
μ
)
for some parameters
λ
,
μ
,
C
λ
,
C
μ
>
0
. In fact, the convergence is monotonic in the sense that both
u
/
u
0
and
v
/
v
0
are decreasing. We also obtain similar results for more general systems.