On the solution of the Poincare boundary value problem for generalised harmonic functions in simply connected domains

In this paper, a boundary value problem of the Poincare type is considered for one second-order elliptic differential equation, generating a class of generalised harmonic functions, in simply connected domains with smooth boundaries. It is established that for sufficiently general assumptions about the coefficients of the boundary value condition of the considered problem, its solution reduces to the sequential solution of the well-studied integro-differential Hilbert boundary value problem and the differential Hilbert boundary value problem in classes of analytic functions of a complex variable. In addition, necessary and sufficient solvability conditions of the considered problem are obtained and its Noetherian property is proved.