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It is shown using the Gross-Pitaevskii equation that resonance states ofBose-Einstein condensates with attractive interactions can be stabilized intotrue bound states. A semiclassical variational approximation and an independentquantum variational numerical method are used to calculate the energies(chemical potentials) and linewidths of resonances of the time-independentGross-Pitaevskii equation; both methods produce similar results. Bordersbetween the regimes of resonances, bound states, and, in two and threedimensions, collapse, are identified.

Transition from resonances to bound states in nonlinear systems: application to Bose–Einstein condensates