  The stability of Bose-Fermi gases trapped in an isotropic potentials at
ultracold temperature is strongly influenced by the interaction between the
fermions and the bosons. At zero temperature, the stability criterion is given
in this paper using variation method, the results show that whether a
fermion-boson mixture is stable depends mainly on the interaction between the
fermions and the bosons. For finite temperature, however, the stability is not
only related to the coupling constants, but also to the temperature. The
stability conditions for finite temperature are also derived and discuss in
details in this paper.
