  The influence of boson-boson and boson-fermion interactions on the stability
of a binary mixture of bosonic and fermionic atoms is investigated. The density
profiles of the trapped mixture are obtained from direct numerical solution of
a modified Gross-Pitaevskii equation that is self-consistently coupled to the
mean-field generated by the interaction with the fermionic species. The
fermions which in turn feel the mean-field created by the bosons are treated in
Thomas-Fermi approximation. We study the effects of different combinations of
signs of the boson-boson and the boson-fermion scattering lengths and determine
explicit expressions for critical particle numbers as function of these
scattering lengths.
