Author:
Chen Wenjing,Huang Xiaomeng
Abstract
Abstract
This paper is concerned with the following biharmonic problem
{
Δ
2
u
=
|
u
|
8
N
−
4
u
in
Ω∖
B
(
ξ
0
,
ε
)
―
,
u
=
Δ
u
=
0
on
∂
(
Ω∖
B
(
ξ
0
,
ε
)
―
)
,
where Ω is an open bounded domain in
R
N
,
N
⩾
5
, and
B
(
ξ
0
,
ε
)
is a ball centered at ξ
0 with radius ɛ, ɛ is a small positive parameter. We obtain the existence of solutions for problem (0.1), which is an arbitrary large number of sign-changing solutions whose profile is a superposition of bubbles with alternate sign which concentrate at the centre of the hole.
Funder
National Natural Science Foundation of China