Existence of Solutions for a Quasilinear Schrödinger Equation with Potential Vanishing
We study the following quasilinear Schrödinger equation − Δ u + V ( x ) u − Δ ( u 2 ) u = K ( x ) g ( u ) , x ∈ ℝ 3 , where the nonlinearity g ( u ) is asymptotically cubic at infinity, the potential V ( x ) may vanish at infinity. Under appropriate assumptions on K ( x ), we establish the existence...
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| Veröffentlicht in: | Acta Mathematicae Applicatae Sinica 2023-07, Vol.39 (3), p.696-706 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study the following quasilinear Schrödinger equation
−
Δ
u
+
V
(
x
)
u
−
Δ
(
u
2
)
u
=
K
(
x
)
g
(
u
)
,
x
∈
ℝ
3
,
where the nonlinearity
g
(
u
) is asymptotically cubic at infinity, the potential
V
(
x
) may vanish at infinity. Under appropriate assumptions on
K
(
x
), we establish the existence of a nontrivial solution by using the mountain pass theorem. |
|---|---|
| ISSN: | 0168-9673 1618-3932 |
| DOI: | 10.1007/s10255-023-1083-2 |