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Catto, I., Dolbeault, J., Sánchez, O. and Soler, J. (2013) Existence of Steady States for the Maxwell-Schrödinger-Poisson System: Exploring the Applicability of the Concentration-Compactness Principle. Mathematical Models and Methods in Applied Sciences, 23, 1915-1938.
https://doi.org/10.1142/s0218202513500541
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
*
.