Nonlinear Poisson-Boltzmann equation in spherical symmetry

The Poisson-Boltzmann problem in spherical symmetry has been considered using the distribution of a self-consistent potential around a charged grain in a thermal collisional plasma as an example. The qualitative patterns of all possible solutions have been presented and a study of their asymptotics has been carried out. It has been demonstrated that for large potentials it is possible to neglect the curvature of the grain surface and to use the solution of the plane problem. It has also been demonstrated that the electrical interaction of the grains is possible only at distances smaller than eight screening lengths