  Equilibrium distribution of interacting ionic particles in a charged
disordered background is studied using the nonlinear Poisson-Boltzmann
equation. For an arbitrarily given realization of the disorder, an exact
solution of the equation is obtained in one dimension using a mapping of the
nonlinear Poisson-Boltzmann equation to a self-consistent Schrodinger equation.
The resulting density profile shows that the ions are delocalized, despite what
the equivalent Schrodinger formulation in one dimension would suggest. It is
shown that the ions are not distributed so as to locally neutralize the
background, presumably due to their mutual interactions.
