On solvability of homogeneous Riemann–Hilbert problem with countable set of coefficient discontinuities and two-side curling at infinity of order less than 1/2

We consider the homogeneous Riemann–Hilbert problem in the complex upper half-plane with a countable set of coefficients' discontinuities and two-side curling at infinity. In the case the problem index has a power singularity of order less than 1/2, we obtain general solution and completely study the solvability of the problem in a special functional class.