On the solutions of mixed plane problems that are unbounded where the boundary conditions change

In this paper, we apply a modification to the method of the integral equation formulation of mixed plane boundary value problems so that it enables us to obtain the solutions unbounded at the points where the boundary conditions change. Such solutions are of great physical interest. The modification is illustrated by means of a typical problem. As is it the case in the original method proposed by Cherskii [1], the problem is reduced to an infinite system of algebraic equations. The justification of the truncation of such systems has been established.