Affiliation:
1. Chongqing Technology and Business University
Abstract
In this paper we study the existence of ground states solutions for
non-autonomous Schrödinger–Bopp–Podolsky system
{
−
Δ
u
+
u
+
λ
K
(
x
)
ϕ
u
=
b
(
x
)
|
u
|
p
−
2
u
in
R
3
,
−
Δ
ϕ
+
a
2
Δ
2
ϕ
=
4
π
K
(
x
)
u
2
in
R
3
,
where
λ
>
0
,
2
<
p
≤
4
and both
K
(
x
)
and
b
(
x
)
are nonnegative
functions in
R
3
. Assuming that
lim
|
x
|
→
+
∞
K
(
x
)
=
K
∞
>
0
and
lim
|
x
|
→
+
∞
b
(
x
)
=
b
∞
>
0
and satisfying suitable assumptions, but not
requiring any symmetry property on them. We show that the existence of a
positive solution depends on the parameters
λ
and
p
. We also
establish the existence of ground state solutions for the case
3.18
≈
1
+
73
3
<
p
≤
4
.
Cited by
2 articles.
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