  Based on the work of Gorling and that of Levy and Nagy, density-functional
formalism for many Fermionic excited-states is explored through a careful and
rigorous analysis of the excited-state density to external potential mapping.
It is shown that the knowledge of the ground-state density is a must to fix the
mapping from an excited-state density to the external potential. This is the
excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the
ground-state density the density of the excited-state gives the true many-body
wavefunctions of the system. Further, the excited-state Kohn-Sham system is
defined by comparing it's non-interacting kinetic energy with the true kinetic
energy. The theory is demonstrated by studying a large number of atomic
systems.
