On sufficient conditions for the positive solvability of the Riemann- Hilbert problem
In a previous paper the author showed that the 21-st Hilbert problem has no solution in a general case. But it is known [see the author, Usp. Mat. Nauk 45, No. 2, 3-47 (1990; Zbl 0706.34005); \textit{V. P. Kostov}, C.R. Acad. Sci., Paris, Ser. I 315, No. 2, 143-148 (1992; Zbl 0772.34007)]that the problem has a solution in the following cases: if a monodromy group lies in GL(2); if a monodromy group is irreducible. A natural question arises in this regard: How can one characterize all monodromy groups such that the Riemann-Hilbert problem is solvable in a positive sense? In the present paper the author has shown that if one can admit the existence of at most one irregular singular point then the problem has a solution. He also indicates new classes of monodromy groups such that the Riemann-Hilbert problem has a positive solution.
scientific article; zbMATH DE number 484233