Abstract
In this article, we investigate the multiplicity results of the following biharmonic Choquard system involving critical nonlinearities with sign-changing weight function:
{
Δ
2
u
=
λ
F
(
x
)
|
u
|
r
−
2
u
+
H
(
x
)
(
∫
Ω
H
(
y
)
|
v
(
y
)
|
2
α
∗
|
x
−
y
|
α
d
y
)
|
u
|
2
α
∗
−
2
u
in
Ω
,
Δ
2
v
=
μ
G
(
x
)
|
v
|
r
−
2
v
+
H
(
x
)
(
∫
Ω
H
(
y
)
|
u
(
y
)
|
2
α
∗
|
x
−
y
|
α
d
y
)
|
v
|
2
α
∗
−
2
v
in
Ω
,
u
=
v
=
∇
u
=
∇
v
=
0
on
∂
Ω
,
where
Ω
is a bounded domain in
R
N
with smooth boundary ∂
Ω
, N≥
5, 1<r<2, 0<α
<N,
2α
∗
=2
N
−
α
N
−
4
is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality and
Δ
2
denotes the biharmonic operator. The functions
F
, G and
H
:
Ω
¯
→
R
are sign-changing weight functions satisfying
F
,
G
∈
L
2
∗
2
∗
−
r
(
Ω
)
and
H
∈
L
∞
(
Ω
)
respectively. By adopting Nehari manifold and fibering map technique, we prove that the system admits at least two nontrivial solutions with respect to parameter
(
λ
,
μ
)
∈
R
+
2
∖
{
(
0
,
0
)
}
.