  The algorithm for generation of exact solutions of the nonlinear equation in
partial derivatives of a divergent type which is included in the formulation of
magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary
Schr\"odinger equation) has been suggested. The properties of smoothness of
solutions in domains with corner points (piecewise smooth boundary) have been
considered. The solutions with unlimited derivatives in the corner point domain
have been presented on the basis of a new class of special functions.
