In this paper, we investigate the following critical elliptic equation
$$-\Delta u+V(y)u=u^{\frac{N+2}{N-2}},\;u>0,\;\text {in}\,{\mathbb {R}}^{N},\;u\in H^{1}({\mathbb {R}}^{N}),$$
where V(y) is a bounded non-negative function in
$${\mathbb {R}}^{N}.$$
Assuming that
$$V(y)=V(|\hat{y}|,y^{*}),y=(\hat{y},y^{*})\in {\mathbb {R}}^{4}\times {\mathbb {R}}^{N-4}$$
and gluing together bubbles with different concentration rates, we obtain new solutions provided that
$$N\ge 7,$$
whose concentrating points are ...
