Boundary value problem with shift for two simply connected regions

Abstract

In this paper a boundary value problem for two analytic functions in different simply connected regions is considered. If index corresponeded to the problem is not greater than zero, then the solavability of that problem is shown without any further conditions and its solution is obtained in an explicit form~(4). However, if the index is greater than zero, then the problem is solvable and its solution is given by~(5) if real conditions of solvability~(6) hold.