  The grand canonical density functional theory for inhomogeneous systems of
interacting bosons is developed in the effective action approach. The Legendre
transform of the generating functional for Green's functions is used to define
the effective action as a functional of both the particle density and the order
parameter. Expanding the thermal effective action in powers of the Planck
constant we obtain a systematic approximation scheme, which practically
implements the Kohn-Sham idea: the problem of interacting bosons is reduced to
a single-particle system in a fictitious external potential. The Kohn-Sham
potential, the density and the order parameter have to be determined
self-consistently in a given order approximation.
