The equations for the distribution functions for systems of charged particles in the medium with inhomogeneities located on sites of a planar crystal lattice are invistigated. In the self-consistent field approximation, the problem of definition of the functions of distribution is reduced to solving the integral equations for the self-consistent potential and the surface density of charges. The existence of a solution of this system of equations is proved in the Hilbert space, whose elements are the pairs of functions.

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