  The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms
is investigated under the assumption of an attractive two-body and a repulsive
three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear
Schr\"odinger equation is extended to include an effective potential dependent
on the square of the density and solved numerically for the $s-$wave. The
lowest frequency of the collective mode is determined through the Fourier
transform of the time dependent solution and its dependences on the number of
atoms and the strength of the three-body force are studied. We show that the
addition of three-body dynamics can allow the number of condensed atoms to
increase considerably, even when the strength of the three-body force is very
small compared with the strength of the two-body force.
