  A collapse of the trapped boson- fermion mixture with the attraction between
bosons and fermions is investigated in the framework of the effective
Hamiltonian for the Bose system. The properties of the $^{87}$Rb and $^{40}$K
mixture are analyzed quantitatively at $T= 0$. We find numerically solutions of
modified Gross- Pitaevskii equation which continuously go from stable to
unstable branch. We discuss the relation of the onset of collapse with
macroscopic properties of the system. A comparison with the case of a Bose
condensate of atomic $^7Li$ system is given.
