Affiliation:
1. Tianjin Chengjian University
Abstract
In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system
{
−
Δ
u
+
V
(
x
)
u
−
(
2
ω
+
ϕ
)
ϕ
u
=
f
(
x
,
u
)
,
x
∈
R
3
,
Δ
ϕ
=
(
ω
+
ϕ
)
u
2
,
x
∈
R
3
,
where
ω
>
0
is a constant and the nonlinearity
f
(
x
,
u
)
is either asymptotically linear in
u
at infinity or the primitive of
f
(
x
,
u
)
is of 4-superlinear growth in
u
at infinity. Under some suitable assumptions, the existence and multiplicity of solutions are proved by using the Mountain Pass theorem and the fountain theorem, respectively.