Abstract
In this paper, we investigate the existence and concentration of solutions for the following Schrödinger–Bopp–Podolsky system with sublinear nonlinearity:
{
−
Δ
u
+
λ
V
(
x
)
u
+
G
(
x
)
ϕ
u
=
f
(
x
,
u
)
in
R
3
,
−
Δ
ϕ
+
a
2
Δ
2
ϕ
=
4
π
G
(
x
)
u
2
in
R
3
,
where
V
∈
C
(
R
3
)
is a potential well,
G
∈
L
2
(
R
3
)
is nonnegative and
f
∈
C
(
R
3
×
R
)
satisfies the sublinear conditions in
R
3
. By imposing some suitable assumptions on
V
(
x
)
,
G
(
x
)
and
f
(
x
,
u
)
, we obtain the existence and multiplicity of negative energy solutions for the above system via variational methods. Moreover, the concentration of solutions is also explored on the set
V
−
(
0
)
as
λ
→
∞
.