TITLE:
Normalized Solutions of the Gross-Pitaevskii System with Inhomogeneous Interactions
AUTHORS:
Rui Sun
KEYWORDS:
Gross-Pitaevskii System, -Critical Exponent, Logarithmic Convolution, Inhomogeneous Interaction
JOURNAL NAME:
Open Access Library Journal,
Vol.13 No.3,
March
5,
2026
ABSTRACT: This paper is devoted to the normalized solutions of the two-dimensional Gross-Pitaevskii system with a microwave field and inhomogeneous interactions. By investigating the relevant
L
2
-critical constrained variational problem, we get the existence and nonexistence of the normalized solutions under suitable assumptions about the interaction potentials. We establish the existence and nonexistence of minimizers of
e(
γ,a
)
via a threshold
a
*
, where
a
*
is the square of
L
2
-norm of the unique positive solution of
Δu−u+
u
3
=0
in
ℝ
2
. We also analyze the limiting behavior of the constraint minimizers as
a↗2
a
*
through overcoming the challenges associated with the sign-changing property of the logarithmic convolutions and the impact of inhomogeneous interactions.