TITLE:
Normalized Solutions to Upper Critical Fractional Kirchhoff-Choquard Type Equations with Potentials
AUTHORS:
Haojia Zhang
KEYWORDS:
Fractional Kirchhoff-Choquard Equation, Normalized Solution, Upper Critical Exponent
JOURNAL NAME:
Open Access Library Journal,
Vol.13 No.3,
March
11,
2026
ABSTRACT: This paper is concerned with the normalized ground state solutions to the following Hardy-Littlewood-Sobolev upper critical fractional Kirchhoff-Choquard type equations under the constraint
∫
ℝ
N
| u |
2
dx
=c
,
(
a+b
∫
ℝ
N
|
(
−Δ
)
s
2
u |
2
dx
)
(
−Δ
)
s
u+V(
x
)u
=λu+μ(
I
θ
∗
| u |
p
)
| u |
p−2
u+(
I
θ
∗
| u |
2
θ,s
*
)
| u |
2
θ,s
*
−2
u in
ℝ
N
,
where
s∈(
0,1
)
,
N∈(
2s,4s
)
,
θ∈(
0,N
)
,
a,b,c,μ>0
,
λ∈ℝ
,
p∈(
N+θ
N
,
N+θ+2s
N
)
and
V
is an external potential vanishing at infinity. Utilizing the perturbed Pohozaev constraint and Schwartz symmetrization rearrangements, we establish the existence of the normalized ground state solutions, and characterize the asymptotic behavior of solutions as
μ→
0
+
in the autonomous case.