  We consider positive solutions of $\Delta u-\mu u+Ku^{\frac{n+2}{n-2}}=0$ on
$B_1$ ($n\ge 5$) where $\mu $ and $K>0$ are smooth functions on $B_1$. If $K$
is very sub-harmonic at each critical point of $K$ in $B_{2/3}$ and the maximum
of $u$ in $\bar B_{1/3}$ is comparable to its maximum over $\bar B_1$, then all
positive solutions are uniformly bounded on $\bar B_{1/3}$. As an application,
a priori estimate for solutions of equations defined on $\mathbb S^n$ is
derived.
