  We studied all possible ground states, including supersolid (SS) phases and
phase separations of hard-core- and soft-core-extended Bose--Hubbard models
with fixed boson densities by using the Gutzwiller variational wave function
and the linear programming method. We found that the phase diagram of the
soft-core model depends strongly on its transfer integral. Furthermore, for a
large transfer integral, we showed that an SS phase can be the ground state
even below or at half filling against the phase separation. We also found that
the density difference between nearest-neighbor sites, which indicates the
density order of the SS phase, depends strongly on the boson density and
transfer integral.
