DOI: 10.1515/dema-2025-0284 ISSN: 2391-4661
On positive solution for Klein–Gordon–Maxwell system of Choquard nonlinearity without polynomial growth conditions
Yu Duan, Xin Sun, Yucheng An Abstract
This article concerns the following Klein–Gordon–Maxwell system with Choquard nonlinearity
−
Δ
u
+
V
(
x
)
u
−
(
2
ω
+
ϕ
)
ϕ
u
=
λ
f
(
u
)
+
I
α
∗
|
u
|
s
|
u
|
s
−
2
u
,
x
∈
R
3
,
Δ
ϕ
=
(
ω
+
ϕ
)
u
2
,
x
∈
R
3
,
$$\begin{cases}-{\Delta}u+V\left(x\right)u-\left(2\omega +\phi \right)\phi u=\lambda f\left(u\right)+\left({I}_{\alpha }\ast \vert u{\vert }^{s}\right)\vert u{\vert }^{s-2}u,\hfill & x\in {\mathbb{R}}^{3},\hfill \\ {\Delta}\phi =\left(\omega +\phi \right){u}^{2},\hfill & x\in {\mathbb{R}}^{3},\hfill \end{cases}$$
where
ω
> 0 is a constant,
λ
> 0 is a parameter,
I
α
is a Riesz potential whose order is
α
and
f
only satisfies superlinear conditions but does not satisfy polynomial growth or Ambrosetti–Rabinowitz conditions. Under certain assumptions on
V
,
α
,
s
, we prove the existence of positive solution using variational methods and Moser iteration. The result extends the related ones in the literature.