R. R. Gontsov, V. A. Poberezhnyi, “Various versions of the Riemann–Hilbert problem for linear differential equations”, Uspekhi Mat. Nauk, 2008, Volume 63, Issue 4(382),Pages <nobr>3

This article is cited in 8 papers

Various versions of the Riemann–Hilbert problem for linear differential equations

R. R. Gontsov^a, V. A. Poberezhnyi^b

^a Institute for Information Transmission Problems, Russian Academy of Sciences
^b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: A counterexample to Hilbert's 21st problem was found by Bolibrukh in 1988 (and published in 1989). In the further study of this problem he substantially developed the approach using holomorphic vector bundles and meromorphic connections. Here the best-known results of the past that were obtained by using this approach (both for Hilbert's 21st problem and for certain generalizations) are presented.

UDC: 517.927.7+517.936

MSC: Primary 34M50; Secondary 34M35, 34M55

Received: 30.06.2008

DOI: 10.4213/rm9230