Affiliation:
1. Northwest Normal University
2. Southwest University
Abstract
In this paper, we study sign-changing solution of the Choquard type equation
−
Δ
u
+
(
λ
V
(
x
)
+
1
)
u
=
(
I
α
∗
|
u
|
2
α
∗
)
|
u
|
2
α
∗
−
2
u
+
μ
|
u
|
p
−
2
u
in
R
N
,
where
N
≥
3
,
α
∈
(
(
N
−
4
)
+
,
N
)
,
I
α
is a Riesz potential,
p
∈
[
2
α
∗
,
2
N
N
−
2
)
,
2
α
∗
:=
N
+
α
N
−
2
is the upper critical exponent in terms of the Hardy–Littlewood–Sobolev inequality,
μ
>
0
,
λ
>
0
,
V
∈
C
(
R
N
,
R
)
is nonnegative and has a potential well. By combining the variational methods and sign-changing Nehari manifold, we prove the existence and some properties of ground state sign-changing solution for
λ
,
μ
large enough. Further, we verify the asymptotic behaviour of ground state sign-changing solutions as
λ
→
+
∞
and
μ
→
+
∞
, respectively.