  It is shown using the Gross-Pitaevskii equation that resonance states of
Bose-Einstein condensates with attractive interactions can be stabilized into
true bound states. A semiclassical variational approximation and an independent
quantum variational numerical method are used to calculate the energies
(chemical potentials) and linewidths of resonances of the time-independent
Gross-Pitaevskii equation; both methods produce similar results. Borders
between the regimes of resonances, bound states, and, in two and three
dimensions, collapse, are identified.
