  In this paper, for any simple, simply connected algebraic group $G$ of type
$B_n,C_n$ or $D_n$ and for any maximal parabolic subgroup $P$ of $G$, we
describe all minimal dimensional Schubert varieties in $G/P$ admitting
semistable points for the action of a maximal torus $T$ with respect to an
ample line bundle on $G/P$. In this paper, we also describe, for any
semi-simple simply connected algebraic group $G$ and for any Borel subgroup $B$
of $G$, all Coxeter elements $\tau$ for which the Schubert variety $X(\tau)$
admits a semistable point for the action of the torus $T$ with respect to a
non-trivial line bundle on
  $G/B$.
