Distribution functions of systems of charged particles in a spatially inhomogeneous medium

The equations for the distribution functions of systems of charged particles in a medium with inhomogeneities are investigated. In the self-consistent field approximation they reduce to nonlinear Poisson–Boltzmann equations with boundary conditions on the surfaces of the inhomogeneities. An analog of the subtractional procedure of quantum field theory is used to prove the existence of a solution.