  We study positive supersolutions to an elliptic equation $(*)$: $-\Delta
u=c|x|^{-s}u^p$, $p,s\in\bf R$ in cone-like domains in $\bf R^N$ ($N\ge 2$). We
prove that in the sublinear case $p<1$ there exists a critical exponent $p_*<1$
such that equation $(*)$ has a positive supersolution if and only if
$-\infty<p<p_*$. The value of $p_*$ is determined explicitly by $s$ and the
geometry of the cone.
