  We study the formation and stability of a single vortex state in a
weakly-interacting Bose-Einstein condensate that is confined in a rotating
harmonic potential. Our results are consistent with the fact that any single
off-center vortex is unstable. Furthermore, a vortex state located at the
center of the cloud first becomes locally stable as the rotational frequency
increases. Finally our study implies the existence of hysteresis effects.
