  In this paper, we consider the following critical polyharmonic equation
\begin{align*}%\label{abs} ( -\Delta)^m
u+V(|y'|,y'')u=Q(|y'|,y'')u^{m^*-1},\quad u>0, \quad y=(y',y'')\in
\mathbb{R}^3\times \mathbb{R}^{N-3},
  \end{align*} where $N>4m+1$, $m\in \mathbb{N}^+$, $m^*=\frac{2N}{N-2m}$,
$V(|y'|,y'')$ and $Q(|y'|,y'')$ are bounded nonnegative functions in
$\mathbb{R}^+\times \mathbb{R}^{N-3}$. By using the reduction argument and
local Poho\u{z}aev identities, we prove that if $Q(r,y'')$ has a stable
critical point $(r_0,y_0'')$ with $r_0>0$, $Q(r_0,y_0'')>0$, $D^\alpha
Q(r_0,y_0'')=0$ for any $|\alpha|\leq 2m-1$ and
$B_1V(r_0,y_0'')-B_2\sum\limits_{|\alpha|=2m}D^\alpha
Q(r_0,y_0'')\int_{\mathbb{R}^N}y^\alpha U_{0,1}^{m^*}dy>0$, then the above
problem has a family of solutions concentrated at points lying on the top and
the bottom circles of a cylinder, where $B_1$ and $B_2$ are positive constants
that will be given later.
