TITLE:
Two Dimensional Schrödinger-Poisson Equation: Existence and Qualitative Properties
AUTHORS:
Dehong Yang
KEYWORDS:
Normalized Solution, Schrödinger-Poisson Equation, Mass-Supercritical, Qualitative Properties
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.10,
October
13,
2026
ABSTRACT: We consider the following two dimensional Schrödinger-Poisson equation
{
−Δu+
| x |
2
u+γφu=λu+a
| u |
p−2
u,
Δφ=
u
2
,
(0.1)where
a,λ∈
ℝ
+
and
p>4
. We prove that problem (0.1) admits a local minimizer
u
p
. Moreover, we investigate the asymptotic behaviour of
u
p
as
p→
4
+
, and establish the stability of the solution.