On solvability of the Hilbert homogeneous boundary value problem for quasiharmonic functions in circular domains

A boundary value problem of the Hilbert type problem in classes of quasi-harmonic functions is considered. A method has been developed for explicitly solving the homogeneous Hilbert problem for quasi-harmonic functions of the first kind in circular domains. In addition, it has been established that the picture of solvability of the problem under consideration essentially depends on whether a unit circle or a circle of non-unit radius is a carrier of the boundary conditions.