  A variational theory is developed to study electrolyte solutions, composed of
interacting point-like ions in a solvent, in the presence of dielectric
discontinuities and charges at the boundaries. Three important and non-linear
electrostatic effects induced by these interfaces are taken into account:
surface charge induced electrostatic field, solvation energies due to the ionic
cloud, and image charge repulsion. Our variational equations thus go beyond the
mean-field theory. The influence of salt concentration, ion valency, dielectric
jumps, and surface charge is studied in two geometries. i) A single neutral
air-water interface with an asymmetric electrolyte. A charge separation and
thus an electrostatic field gets established due to the different image charge
repulsions for coions and counterions. Both charge distributions and surface
tension are computed and compared to previous approximate calculations. For
symmetric electrolyte solutions close to a charged surface, two zones are
characterized. In the first one, with size proportional to the logarithm of the
coupling parameter, strong image forces impose a total ion exclusion, while in
the second zone the mean-field approach applies. ii) A symmetric electrolyte
confined between two dielectric interfaces as a simple model of ion rejection
from nanopores. The competition between image charge repulsion and attraction
of counterions by the membrane charge is studied. For small surface charge, the
counterion partition coefficient decreases with increasing pore size up to a
critical pore size, contrary to neutral membranes. For larger pore sizes, the
whole system behaves like a neutral pore. The prediction of the variational
method is also compared with MC simulations and a good agreement is observed.
