  Using variational and numerical solutions we show that stationary
negative-energy localized (normalizable) bound states can appear in the
three-dimensional nonlinear Schr\"odinger equation with a finite square-well
potential for a range of nonlinearity parameters. Below a critical attractive
nonlinearity, the system becomes unstable and experiences collapse. Above a
limiting repulsive nonlinearity, the system becomes highly repulsive and cannot
be bound. The system also allows nonnormalizable states of infinite norm at
positive energies in the continuum. The normalizable negative-energy bound
states could be created in BECs and studied in the laboratory with present
knowhow.
