14-08E

The phase transitions in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations, in the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction, are investigated. The behavior of the BE condensate order parameter and grand canonical potential as functions of the chemical potential of bosons is analyzed. The possibility of change of order of the phase transition to the superfluid phase in certain range of the values of the chemical potentials of Bose- and Fermi-particles is established. For the cases $T=0$ and $T\not =0$ the phase diagrams in the plane (temperature, boson chemical potential) for different values of parameters of boson transfer and chemical potential of fermions $\mu '$ are built.