  In this paper, a new analysis for existence, uniqueness, and regularity of
solutions to a time-dependent Kohn-Sham equation is presented. The Kohn-Sham
equation is a nonlinear integral Schroedinger equation that is of great
importance in many applications in physics and computational chemistry. To deal
with the time-dependent, nonlinear and non-local potentials of the Kohn-Sham
equation, the analysis presented in this manuscript makes use of energy
estimates, fixed-point arguments, regularization techniques, and direct
estimates of the non-local potential terms. The assumptions considered for the
time-dependent and nonlinear potentials make the obtained theoretical results
suitable to be used also in an optimal control framework.
