On solvability of homogeneous Riemann–Hilbert problem with discontinuities of coefficients and two-side curling at infinity of a logarithmic order

We consider the homogeneous Riemann–Hilbert boundary-value problem for upper half-plane in the situation where its coefficients have countable set of discontinuities of jump type and two-side curling at infinity of a logarithmic order. We obtain general solution and describe completely its solvability in a special class of functions for the case where the index of the problem has power singularity of a logarithmic order.