  The LSDA+U approach to density functional theory is carefully reanalyzed. Its
possible link to single-particle Green's function theory is occasionally
discussed. A simple and elegant derivation of the important sum rules for the
on-site interaction matrix elements linking them to the values of U and J is
presented. All necessary expressions for an implementation of LSDA+U into a
non-orthogonal basis solver for the Kohn-Sham equations are given, and
implementation into the FPLO solver is made. Results of application to several
planar cuprate structures are reported in detail and conclusions on the
interpretation of the physics of the electronic structure of the cuprates are
drawn.
