This article continues earlier work of the author on non-linear systems of ordinary differential equations, published in Asymptotic Analysis 15 (1997), MR no. 98g:34015b. There, a completely formal theory was presented, while here we are concerned with a semi-formal approach: Solutions of non-linear systems of ordinary meromorphic differential equations are represented as, in general divergent, power series in several free parameters. The coefficients, aside from an exponential polynomial, a general...

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.