  The electrostatic Schwinger-Dyson equations are derived and solved for an
electrolyte mixture composed of mono- and multivalent ions confined to a
negatively charged nanoslit. The closure of these equations is based on an
asymmetric treatment of the ionic species with respect to their electrostatic
coupling strength; the weakly coupled monovalent ions are treated within a
gaussian approximation while the multivalent counterions of high coupling
strength are incorporated with a strong-coupling approach. The resulting
self-consistent formalism includes explicitly the interactions of the
multivalent counterions with the monovalent salt. In highly charged membranes
characterized by a pronounced multivalent counterion adsorption, these
interactions take over the salt-membrane charge coupling. As a result, the
increment of the negative membrane charge brings further salt anions into the
pore and excludes salt cations from the pore into the reservoir. The
corresponding like-charge attraction and opposite-charge repulsion effect is
amplified by the pore confinement but suppressed by salt addition into the
reservoir. The effect is particularly pronounced in high dielectric membranes
where the attractive polarization forces lead to a dense multivalent cation
layer at the membrane walls. These cation layers act as an effective positive
surface charge, resulting in a total monovalent cation exclusion and a strong
anion excess even in the case of neutral membrane walls.
