  We consider the following prescribed scalar curvature equations in
${\mathbb{R}}^N$ $$
  - \Delta u =K(|y|)u^{2^*-1},\quad u>0 \quad \mbox{in} \quad {\mathbb{R}}^N,
\quad u \in D^{1, 2}({\mathbb{R}}^N), $$ where $K(r)$ is a positive function,
$2^*=\frac{2N}{N-2}$. We modify the methods and improve the results in [15].
