Multi-peak positive solutions for a logarithmic Schrödinger equation via variational methods
In this paper, using the variational methods, we show the existence and multiplicity of multi-peak positive solutions for the following logarithmic Schrödinger equation: { − ϵ 2 Δ u + V ( x ) u = u log u 2 , i n ℝ N , u ∈ H 1 ( ℝ N ) , where ϵ > 0, N ≥ 2 and V : ℝ N → ℝ is a multi-well potential....
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| Veröffentlicht in: | Israel journal of mathematics 2024-03, Vol.259 (2), p.835-885 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, using the variational methods, we show the existence and multiplicity of multi-peak positive solutions for the following logarithmic Schrödinger equation:
{
−
ϵ
2
Δ
u
+
V
(
x
)
u
=
u
log
u
2
,
i
n
ℝ
N
,
u
∈
H
1
(
ℝ
N
)
,
where ϵ > 0,
N
≥ 2 and
V
: ℝ
N
→ ℝ is a multi-well potential. |
|---|---|
| ISSN: | 0021-2172 1565-8511 |
| DOI: | 10.1007/s11856-023-2494-8 |