  We investigate the nonlocal Gross-Pitaevskii (GP) equation with long-range
dipole-dipole and contact interactions (including binary and three-body
collisions). We address the impact of the three-body interaction on stabilizing
trapless dipolar Bose-Einstein condensates (BECs). It is found that the dipolar
BECs exhibit stability not only for the usual combination of attractive binary
and repulsive three-body interactions, but also for the case when these terms
have opposite signs. The trapless stability of the dipolar BECs may be further
enhanced by time-periodic modulation of the three-body interaction imposed by
means of Feshbach resonance. The results are produced analytically using the
variational approach and confirmed by numerical simulations.
