  We investigate, within a local density functional theory formalism, the
interactions between like-charged polyions immersed in a confined electrolyte.
We obtain a simple condition for a repulsive effective pair potential, that can
be related to the thermodynamic stability criterion of the uncharged
counterpart of microscopic species constituting the electrolyte. Under the same
condition, the phenomenon of charge inversion (over-charging), where the
polyion bare charge is over-screened by its electric double layer, is shown to
be impossible. These results hold beyond standard mean-field theories (such as
Poisson-Boltzmann or Modified Poisson-Boltzmann approaches).
