Nonexistence of stable solutions for quasilinear Schrödinger equation
In this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1 − Δ u − [ Δ ( 1 + u 2 ) 1 / 2 ] u 2 ( 1 + u 2 ) 1 / 2 = h ( x ) | u | q − 1 u , x ∈ R N , where N ≥ 3 , q ≥ 5 / 2 and the function h ( x ) is continuous and positive in R N . Under suitable assu...
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| Veröffentlicht in: | Boundary value problems 2018-11, Vol.2018 (1), p.1-11, Article 168 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation
0.1
−
Δ
u
−
[
Δ
(
1
+
u
2
)
1
/
2
]
u
2
(
1
+
u
2
)
1
/
2
=
h
(
x
)
|
u
|
q
−
1
u
,
x
∈
R
N
,
where
N
≥
3
,
q
≥
5
/
2
and the function
h
(
x
)
is continuous and positive in
R
N
. Under suitable assumptions on
h
(
x
)
and
q
, we prove that Eq. (
0.1
) has no nonnegative and stable solutions. |
|---|---|
| ISSN: | 1687-2770 1687-2762 1687-2770 |
| DOI: | 10.1186/s13661-018-1087-7 |