  Phase transitions are investigated in the Bose-Fermi-Hubbard model in the
mean field and hard-core boson approximations for the case of infinitely small
fermion transfer and repulsive on-site boson-fermion interaction. The behavior
of the Bose-Einstein condensate order parameter and grand canonical potential
is analyzed as functions of the chemical potential of bosons at zero
temperature. The possibility of change of order of the phase transition to the
superfluid phase in the regime of fixed values of the chemical potentials of
Bose- and Fermi-particles is established. The relevant phase diagrams are
built.
