TITLE:
Normalized Solutions for the Kirchhoff-Schrödinger Systems with Weakly Attractive Potentials
AUTHORS:
Wenhao Tu, Li Wang, Li Chen
KEYWORDS:
Schrödinger Systems, Normalized Solutions, Weakly Attractive Potentials, Variational Method, Pohoaev Manifold
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.12,
December
23,
2025
ABSTRACT: In this paper, we consider the following Kirchhoff-Schrödinger system with weakly attractive potentials:
{
−(
a+b
∫
ℝ
N
|
∇
u
1
|
2
dx
)Δ
u
1
+
V
1
u
1
=
λ
1
u
1
+
ν
1
|
u
1
|
p
1
−2
u
1
+α
q
1
|
u
1
|
q
1
−2
u
1
|
u
2
|
q
2
,
−(
a+b
∫
ℝ
N
|
∇
u
2
|
2
dx
)Δ
u
2
+
V
2
u
2
=
λ
2
u
2
+
ν
2
|
u
2
|
p
2
−2
u
2
+α
q
2
|
u
1
|
q
1
|
u
2
|
q
2
−2
u
2
,
having prescribed mass
∫
ℝ
N
|
u
i
|
2
dx
=
m
i
, where
a>0
,
b,α,
ν
i
>0
,
q
i
>1
,
N=2,3
,
λ
i
∈ℝ
are Lagrange multiplier and
V
i
∈
C
1
(
ℝ
N
)
are potential functions for
i=1,2
. When
2+
8
N
<
q
1
+
q
2
<
2
*
and
(
p
1
,
p
2
)∈
ℝ
2
, we prove the existence of multiple solutions, which are positive radial vectors.
2
*
=
2N/
(
N−2
)
is the Sobolev critical exponent. The proof is based on variational techniques and constrained minimization arguments.