We study the following nonlinear critical elliptic equation
$$\begin{aligned} -\Delta u+\epsilon Q(y)u=u^{\frac{N+2}{N-2}},\;\;\; u>0\;\;\;\hbox { in } {\mathbb {R}}^N, \end{aligned}$$
where
$$\epsilon >0$$
is small and
$$N\ge 5.$$
Assuming that Q(y) is periodic in
$$y_1$$
with period 1 and has a local minimum at 0 satisfying
$$Q(0)>0,$$
we prove the existence and local uniqueness of infinitely many bubbling solutions of it. This local uniqueness result implies that some bubbling solutions preserve the symmetry of the potential function Q(...
