  We construct a density functional theory for two-dimension electron (hole)
gases subjected to both strong magnetic fields and external potentials. In
particular, we are focused on regimes near even-denominator filling factors, in
which the systems form composite fermion liquids. Our theory provides a
systematic and rigorous approach to determine the properties of ground states
in fractional quantum Hall regime modified by artificial structures. We also
propose a practical way to construct approximated functional.
