  Multiple phases occurring in a Bose gas with finite-range interaction are
investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC)
the chemical potential and the pressure show a van-der-Waals like behavior
indicating a first-order phase transition although there is no long-range
attraction. Furthermore the equation of state becomes multivalued near the BEC
transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation
such a multivalued region can be avoided by the Maxwell construction. For
sufficiently weak interaction the multivalued region can also be removed using
a many-body \mbox{T-matrix} approximation. However, for strong interactions
there remains a multivalued region even for the \mbox{T-matrix} approximation
and after the Maxwell construction, what is interpreted as a density
hysteresis. This unified treatment of normal and condensed phases becomes
possible due to the recently found scheme to eliminate self-interaction in the
\mbox{T-matrix} approximation, which allows to calculate properties below and
above the critical temperature.
