Solvability homogeneous Riemann-Hilbert boundary value problem with several points of turbulence

We consider the so called Hilbert boundary value problem with infinite index in the unit disk. Its coefficient is assumed to be Hölder-continuous everywhere on the unit circle excluding a finite set of points. At these points its argument has power discontinuities of orders less than one. We obtain formulas for the general solution and describe completely the solvability picture in a special functional class. Our technique is based on the theory of entire functions and the geometric theory of functions.