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Abstract

In this article, we consider the boundary value problem of the type of the Hilbert problem in classes of quasiharmonic functions of the second kind. The stability of solutions Hilbert boundary value problem in classes of quasiharmonic functions of the second kind with respect to the change in the radius of the considered circular domain is analyzed. Based on the theory of boundary value problems of complex analysis and the analytic theory of differential equations, the construction of a solvability picture of the homogeneous Hilbert problem in classes of quasiharmonic functions of the second kind in circular domains. The main reason for the instability of solutions of the Hilbert boundary value problem are the singularities of the solution of the Euler differential equation. In particular, it is proved that the number of linearly independent solutions of the problem under consideration Hilbert problem essentially depends on the region of radius of the region under consideration. Сведения об авторах: Расулов Карим Магомедович – доктор физико-математических наук, профессор, заведующий кафедрой математического анализа Смоленского государственного университета, kahrimanr@yandex.ru Тимофеева Татьяна Игоревна – магистрант физико-математического факультета Смоленского государственного университета, tat.timopheeva@yandex.ru