Abstract
This article concerns the following Klein–Gordon–Maxwell systems with the term of Choquard
{
−
Δ
u
+
V
(
x
)
u
−
(
2
ω
+
ϕ
)
ϕ
u
=
f
(
x
,
u
)
+
(
I
α
∗
|
u
|
p
)
|
u
|
p
−
2
u
,
x
∈
R
3
,
Δ
ϕ
=
(
ω
+
ϕ
)
u
2
,
x
∈
R
3
,
and
{
−
Δ
u
+
V
(
x
)
u
−
(
2
ω
+
ϕ
)
ϕ
u
=
λ
|
u
|
q
−
2
u
+
(
I
α
∗
|
u
|
p
)
|
u
|
p
−
2
u
,
x
∈
R
3
,
Δ
ϕ
=
(
ω
+
ϕ
)
u
2
,
x
∈
R
3
,
where
ω
>
0
is a constant,
λ
>
0
is a parameter,
q
≥
6
,
I
α
is a Riesz potential whose order is
α
. Under some suitable assumptions on
α
,
p
,
V
and
f
, we establish the existence and multiplicity of solutions for the systems by variational methods and Moser iteration. Our results extend several recent findings on solutions to these systems.