This article is cited in 3 papers

Brief communications

A homogeneous Hilbert problem with discontinuous coefficients and two-side curling at infinity of order $1/2\leq\rho<1$

R. B. Salimov, P. L. Shabalin

Chair of Higher Mathematics, Kazan State University of Architecture and Engineering, Kazan, Russia

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 $\rho$, $1/2\leq\rho<1$, and study the solvability conditions.

Keywords: Riemann–Hilbert boundary value problem, curling at infinity, entire functions.

UDC: 517.54

Received: 17.06.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:11, 58–61

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