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The Existence and Blow-Up of the Radial Solutions of a (k1, k2)-Hessian System Involving a Nonlinear Operator and Gradient
In this paper, we are concerned with the existence of the positive bounded and blow-up radial solutions of the ( k 1 , k 2 )-Hessian system { G ( K 1 1 k 1 ) K 1 1 k 1 = b 1 ( | x ∣ ) g 1 ( z 1 , z 2 ) , x ∈ ℝ N , G ( K 2 1 k 2 ) K 2 1 k 2 = b 2 ( | x | ) g 2 ( z 1 , z 2 ) , x ∈ ℝ N , where G is a n...
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| Published in: | Acta mathematica scientia 2022-04, Vol.42 (4), p.1414-1426 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | In this paper, we are concerned with the existence of the positive bounded and blow-up radial solutions of the (
k
1
,
k
2
)-Hessian system
{
G
(
K
1
1
k
1
)
K
1
1
k
1
=
b
1
(
|
x
∣
)
g
1
(
z
1
,
z
2
)
,
x
∈
ℝ
N
,
G
(
K
2
1
k
2
)
K
2
1
k
2
=
b
2
(
|
x
|
)
g
2
(
z
1
,
z
2
)
,
x
∈
ℝ
N
,
where
G
is a nonlinear operator,
K
i
=
S
k
i
(
λ
(
D
2
z
i
)
)
+
ψ
i
(
|
x
|
)
|
∇
z
i
|
k
i
,
i
=
1
,
2
. Under the appropriate conditions on
g
1
and
g
2
, our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem. Furthermore, our main results also extend the previous existence results for both the single equation and systems. |
|---|---|
| ISSN: | 0252-9602 1572-9087 |
| DOI: | 10.1007/s10473-022-0409-0 |