Article citationsMore>>
Garnier, J., Baudin, K., Fusaro, A. and Picozzi, A. (2021) Incoherent Localized Structures and Hidden Coherent Solitons from the Gravitational Instability of the Schrödinger-Poisson Equation. Physical Review E, 104, Article ID: 054205.
https://doi.org/10.1103/physreve.104.054205
has been cited by the following article:
-
TITLE:
Normalized Solutions for a Planar Schrödinger-Poisson System with Inhomogeneous Attractive Interactions
AUTHORS:
Qi Xue
KEYWORDS:
Schrödinger-Poisson System, Logarithmic Convolution, Inhomogeneous Attractive Interaction, Normalized Solution
JOURNAL NAME:
Open Access Library Journal,
Vol.12 No.4,
April
8,
2025
ABSTRACT: This paper is devoted to the normalized solutions of a planar
L
2
-critical Schrödinger-Poisson system with an external potential
V(
x
)=
| x |
2
and inhomogeneous attractive interactions
K(
x
)∈(
0,1
)
. Applying the constraint variational method, we prove that the normalized solutions exist if and only if the interaction strength
a
satisfies
a∈(
0,
a
*
):=
‖ Q ‖
L
2
(
ℝ
2
)
2
, where
Q
is the unique positive solution of
Δu−u+
u
3
=0
in
ℝ
2
. Particularly, the refined limiting behavior of positive minimizers is also analyzed as
a↗
a
*
.