A homogeneous Hilbert problem with discontinuous coefficients and two-side curling at infinity point of order 1/2 ≤ ρ < 1

Abstract

We study a homogeneous Riemann—Hilbert boundary-value problem in the upper half of the complex plane with a countable set of coefficient discontinuities and two-side curling at infinity. We obtain a general solution in the case when the problem index has a power singularity of order ρ, 1/2 ≤ ρ < 1, and study the solvability conditions.