Affiliation:
1. East China University of Science and Technology
2. AGH University of Science and Technology
3. University of Craiova
Abstract
In this paper, we are concerned with the following magnetic Schrödinger–Poisson system
{
−
(
∇
+
i
A
(
x
)
)
2
u
+
(
λ
V
(
x
)
+
1
)
u
+
ϕ
u
=
α
f
(
|
u
|
2
)
u
+
|
u
|
4
u
,
in
R
3
,
−
Δ
ϕ
=
u
2
,
in
R
3
,
where
λ
>
0
is a parameter,
f
is a subcritical nonlinearity, the potential
V
:
R
3
→
R
is a continuous function verifying some conditions, the magnetic potential
A
∈
L
l
o
c
2
(
R
3
,
R
3
)
. Assuming that the zero set of
V
(
x
)
has several isolated connected components
Ω
1
,
…
,
Ω
k
such that the interior of
Ω
j
is non-empty and
∂
Ω
j
is smooth, where
j
∈
{
1
,
…
,
k
}
, then for
λ
>
0
large enough, we use the variational methods to show that the above system has at least
2
k
−
1
multi-bump solutions.
Cited by
2 articles.
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