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 for...

We review some of the basic mathematical results about density functional theory.

A formalism to describe steady-state electronic and thermal transport in the framework of density functional theory is presented. one-to-one correspondence proven between three basic variables theory, i.e., on as well electrical heat currents through junction, potentials, local potential DC bias gradient across junction. Consequently, Kohn-Sham system requires exchange-correlations potentials. ...