  A time-dependent Kohn-Sham (KS) like theory is presented for N bosons in thre
e and lower-dimensional traps. We derive coupled equations, which allow one to
calculate the energies of elementary excitations. A rigorous proof is given to
show that the KS like equation correctly describes properties of the
one-dimensional condensate of impenetrable bosons in a general time-dependent
harmonic trap in the larg N limit.
