Some problems in density functional theory

Though calculations based on density functional theory (DFT) are used remarkably widely in chemistry, physics, materials science, and biomolecular research though the modern form of DFT has been studied for almost 60 years, some mathematical problems remain. For context, we provide an outline basic structure DFT, then pose several questions regarding both its time-independent time-dependent forms. Progress any these would aid development better approximate functionals interpretation.