  Using the Bethe ansatz method, we study the ground state properties of a
$U\to\infty$ Anderson impurity in a ``gapless'' host, where a density of band
states vanishes at the Fermi level $\epsilon_F$ as $|\epsilon-\epsilon_F|$. As
in metals, the impurity spin is proven to be screened at arbitrary parameters
of the system. However, the impurity occupancy as a function of the bare
impurity energy is shown to acquire novel qualitative features which
demonstrate a nonuniversal behavior of the system. The latter explains why the
Kondo screening is absent (or exists only at quite a large electron-impurity
coupling) in earlier studies based on scaling arguments.
