  Thermodynamic properties of a system of interacting boson particles and
antiparticles at finite temperatures are studied within the framework of the
thermodynamically consistent Skyrme-like mean-field model. The mean field
contains both attractive and repulsive terms. Self-consistency relations
between the mean field and thermodynamic functions are derived. We assume
conservation of the isospin density for all temperatures. It is shown that,
independently of the strength of the attractive mean field, at the critical
temperature $T_{\rm c}$ the system undergoes the phase transition of
second-order to the Bose-Einstein condensate, which exists in the temperature
interval $0 \le T \le T_{\rm c}$. We obtained that the condensation represents
a discontinuity of the derivative of the heat capacity at $T = T_{\rm c}$, and
condensate occurs only for the component with a higher particle-number density
in the particle-antiparticle system.
