Geodesic
To a~solution of the inhomogeneous Riemann--Hilbert boundary value problem for analytic function in multiconnected circular domain in a~special case
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 3, pp. 52-58

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The author offers a new approach to solution of the Riemann–Hilbert boundary value problem for analytic function in multiconnected circular domain. This approach is based on construction of solution of corresponding homogeneous problem, when analytic in domain function is being defined by known boundary values of its argument. The author considers a special case of a problem when the index of a problem is more than zero and on unit of less order of connectivity of domain. Resolvability of a problem depends on number of solutions of some system of the linear algebraic equations. 
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     author = {R. B. Salimov},
     title = {To a~solution of the inhomogeneous {Riemann--Hilbert} boundary value problem for analytic function in multiconnected circular domain in a~special case},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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R. B. Salimov. To a~solution of the inhomogeneous Riemann--Hilbert boundary value problem for analytic function in multiconnected circular domain in a~special case. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 3, pp. 52-58. http://geodesic.mathdoc.fr/item/ISU_2013_13_3_a6/