  We obtain, using the Birman-Schwinger method, upper limits on the total
number of bound states and on the number of $\ell$-wave bound states of the
semirelativistic spinless Salpeter equation. We also obtain a simple condition,
in the ultrarelativistic case ($m=0$), for the existence of at least one
$\ell$-wave bound states: $C(\ell,p/(p-1))$ $\int_0^{\infty}dr r^{p-1}
|V^-(r)|^p\ge 1$, where $C(\ell,p/(p-1))$ is a known function of $\ell$ and
$p>1$.
