  We investigate the stability of the Bose-Einstein condensate (BEC) the case
of atoms with negative scattering lengths at zero temperature using the
Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact
equation for determining the upper bound of the critical numbers $N_{cr}$ of
atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for
Bose-Einstein condensation of lithium atoms based on our new equation is in
agreement with those observed in a agreement with those observed in a recent
experiment.
