TITLE:
Normalized Solutions to Fractional Kirchhoff-Choquard Type Equations with the Lower Critical Exponent
AUTHORS:
Haojia Zhang
KEYWORDS:
Fractional Kirchhoff-Choquard Equation, Normalized Solution, Lower Critical Exponent
JOURNAL NAME:
Open Access Library Journal,
Vol.12 No.9,
September
25,
2025
ABSTRACT: This paper is concerned with the normalized ground states to the following lower critical fractional Kirchhoff-Choquard type equations under the constraint
∫
ℝ
N
| u |
2
dx
=
c
2
,
(
a+b
∫
ℝ
N
|
(
−Δ
)
s
2
u |
2
dx
)
(
−Δ
)
s
u−λu
=(
I
θ
∗
| u |
N+θ
N
)
| u |
N+θ
N
−2
u+μ(
I
θ
∗
| u |
q
)
| u |
q−2
u in
ℝ
N
,
where
s∈(
0,1
)
,
N∈(
2,4 ]
,
θ∈(
0,N
)
,
a,b,c,μ>0
,
q∈(
N+θ
N
,
N+θ+2s
N
)
,
λ∈ℝ
appears as a Lagrange multiplier and
I
θ
is the Riesz potential. Using the constraint variational method, we establish the existence of normalized ground states and analyze their asymptotic properties as
μ→
0
+
or
c→
0
+
.