Affiliation:
1. East China Jiaotong University
2. Sun Yat-sen University
3. Hubei University of Arts and Science
Abstract
In this paper, we study the existence of multi-bump solutions for the following Schrödinger–Bopp–Podolsky system with steep potential well:
{
−
Δ
u
+
(
λ
V
(
x
)
+
V
0
(
x
)
)
u
+
K
(
x
)
ϕ
u
=
|
u
|
p
−
2
u
,
x
∈
R
3
,
−
Δ
ϕ
+
a
2
Δ
2
ϕ
=
K
(
x
)
u
2
,
x
∈
R
3
,
where
p
∈
(
4
,
6
)
,
a
>
0
and
λ
is a parameter. We require that
V
(
x
)
≥
0
and has a bounded potential well
Ω
=
V
−
1
(
0
)
. Combining this with other suitable assumptions on
Ω
,
V
0
and
K
, when
λ
is large enough, we obtain the existence of multi-bump-type solutions
u
λ
by using variational methods.
Funder
National Natural Science Foundation of China