TITLE:
Existence and Stability of Standing Waves for the Inhomogeneous Schrödinger Equations with Mixed Fractional Laplacians
AUTHORS:
Wenlong Du
KEYWORDS:
Laplace Operator, Existence, Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
17,
2025
ABSTRACT: In this paper, we consider the existence and orbital stability of standing waves for the inhomogeneous Schrödinger equations with mixed fractional Laplacians
i
∂
t
ψ−
(
−Δ
)
s
1
ψ−
(
−Δ
)
s
2
ψ+
| x |
−γ
| ψ |
2σ
ψ=0, (
t,x
)∈[
0,T )×
ℝ
N
,
where
N≥2
,
0<
s
2
<
s
1
<1
, and
0<γ<2
s
1
. In the
L
2
-subcritical case, i.e.,
0<σ<
2
s
1
−γ
N
, we establish the existence and orbital stability of standing waves. Our approach is based on the concentration-compactness principle in the fractional Sobolev spaces
H
s
1
for
s
1
∈(
0,1
)
.