A long standing problem of solid state theory is solved, being the der
ivation of a set of self-consistent one-particle equations for the int
eracting multicomponent hole gas of a semiconductor in an external pot
ential. Combining effective mass theory with density functional theory
, the Hohenberg-Kohn theorem is generalized and a set of generalized K
ohn-Sham equations is obtained for the multicomponent gas. It is demon
strated how the exchange-correlation potential matrix may be calculate
d by the local density approximation. Explicit results are given for t
he Gamma(8) valence band holes of zinc blende type semiconductors. [S0
031-9007(97)04490-6].