Abstract
In this paper, we investigate the existence of ground state sign-changing solutions for Kirchhoff-type equation with critical exponent
−
(
a
+
b
∫
ℝ
3
|
∇
u
|
2
d
x
)
Δ
u
+
λ
V
(
x
)
u
=
|
u
|
4
u
+
μ
f
(
u
)
,
x
∈
ℝ
3
,
where
a
,
b
,
μ
,
λ
>
0
are positive parameters. Under suitable conditions on
f
and
V
, by working on a sign-changing Nehari manifold and combining minimax arguments with deformation techniques, we establish the existence of least energy sign-changing solutions. At the same time, we also study the asymptotic behavior of sign-changing solutions as
λ
→
∞
.