The stability criteria are obtained for arbitrary localized perturbati
ons in the plane of a stellar disk. The complete stabilization require
s that Toomre's stability parameter Q be greater than the critical par
ameter Q(c) calculated as a function of the parameter alpha(2) = 2 Ohm
/r\Ohm'\, which characterizes the extent to which the disk rotation is
differential. In particular, for the most interesting case of a flat
rotation curve (alpha(2) = 2), the quantity Q(c) turns out to be a uni
versal constant (Q(c) approximate to 3.15). The criteria for disk stab
ility relative to bending of its plane are also briefly discussed.