  Let $u_1$ and $u_2$ be two different positive smooth solutions of the
equation $\Delta u + n (n - 2) u^{{n + 2}\over {n - 2}} = 0$ in $R^n (n \ge
3).$ By a result of Gidas, Ni and Nirenberg, $u_1$ and $u_2$ are radially
symmetric above the points $\xi_1$ and $\xi_2$, respectively. Let $u$ be a
positive $C^2$-function on $R^n$ such that $u = u_1$ in $\Omega_1$ and $u =
u_2$ in $\Omega_2$, where $\Omega_1$ and $\Omega_2$ are disjoint non-empty open
domains in ${\R}^n$. $u$ satisfies the equation $\Delta u + n (n - 2) K u^{{n +
2}\over {n - 2}} = 0$ in $R^n.$ By the same result of Gidas, Ni and Nirenberg,
$K \not\equiv 1$ in $R^n$. In this paper we discuss lower bounds on
$\displaystyle{\sup_{\R^n} |K - 1|} .$ Relation with decay estimates at the
isolated singularity via the Kelvin transform is also considered.
