On a power-type coupled system with mean curvature operator in Minkowski space
We study the Dirichlet problem for the prescribed mean curvature equation in Minkowski space { M ( u ) + v α = 0 in B , M ( v ) + u β = 0 in B , u | ∂ B = v | ∂ B = 0 , where M ( w ) = div ( ∇ w 1 − | ∇ w | 2 ) and B is a unit ball in R N ( N ≥ 2 ) . We use the index theory of fixed points for com...
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| Veröffentlicht in: | Boundary value problems 2021-11, Vol.2021 (1), p.1-9, Article 95 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study the Dirichlet problem for the prescribed mean curvature equation in Minkowski space
{
M
(
u
)
+
v
α
=
0
in
B
,
M
(
v
)
+
u
β
=
0
in
B
,
u
|
∂
B
=
v
|
∂
B
=
0
,
where
M
(
w
)
=
div
(
∇
w
1
−
|
∇
w
|
2
)
and
B
is a unit ball in
R
N
(
N
≥
2
)
. We use the index theory of fixed points for completely continuous operators to obtain the existence, nonexistence and uniqueness results of positive radial solutions under some corresponding assumptions on
α
,
β
. |
|---|---|
| ISSN: | 1687-2770 1687-2762 1687-2770 |
| DOI: | 10.1186/s13661-021-01572-z |