We revisit the well known prescribed scalar curvature problem
$$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=\big (1+\varepsilon K(x)\big )u^{2^*-1}, u(x)>0,~~ &{}{x\in \mathbb {R}^N},\\ u\in \mathcal {D}^{1,2}(\mathbb {R}^N),\\ \end{array}\right. } \end{aligned}$$
where
$$2^*=\frac{2N}{N-2}$$
,
$$N\ge 5$$
,
$$\varepsilon >0$$
and
$$K(x)\in C^1(\mathbb {R}^N)\cap L^{\infty }(\mathbb {R}^N)$$
. It is known that there are a number of results related to the existence of solutions conce...
