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Some addition to the generalized Riemann-Hilbert problem

R.R. GontsovI.V. Vyugin — 2009

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be non-minimal, the problem is known to have a solution. In this article we give a bound for the possibly non-minimal Poincaré rank. We also give a bound for the number of apparent singularities of a scalar equation with prescribed generalized monodromy data.

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