Orbital Stability of Nonlinear Schrödinger–Kirchhoff Equations
In this paper, we study the following equations 0.1 i ϕ t = - A ( | | ∇ ϕ | | 2 ) Δ ϕ - | ϕ | p - 1 ϕ , t > 0 , x ∈ R n , ϕ ( x , 0 ) = ϕ 0 ( x ) ∈ H 1 ( R n ) , where n ≥ 1 , 1 < p < n + 4 n , A ( s ) is a function. Under suitable conditions on A ( s ), we use Lyapunov method to prove the...
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| Veröffentlicht in: | Mediterranean journal of mathematics 2022-02, Vol.19 (1), Article 36 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we study the following equations
0.1
i
ϕ
t
=
-
A
(
|
|
∇
ϕ
|
|
2
)
Δ
ϕ
-
|
ϕ
|
p
-
1
ϕ
,
t
>
0
,
x
∈
R
n
,
ϕ
(
x
,
0
)
=
ϕ
0
(
x
)
∈
H
1
(
R
n
)
,
where
n
≥
1
,
1
<
p
<
n
+
4
n
,
A
(
s
) is a function. Under suitable conditions on
A
(
s
), we use Lyapunov method to prove the orbital stability of standing wave for (
0.1
). |
|---|---|
| ISSN: | 1660-5446 1660-5454 |
| DOI: | 10.1007/s00009-021-01969-1 |