Uniqueness of asymptotic solutions for linear systems of ODEs with isolated singularities of general type

D. Guzzetti<sup>ab

a</sup> INFN — National Institute of Nuclear Physics, Sezione di Trieste, Trieste, Italy
^b Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy

Abstract: This article is a review of our paper [18] which, for a wide class of ODEs, provides sufficient conditions of existence and uniqueness of a fundamental system of solutions, with specified asymptotic behaviour, in wide sectors centered at an isolated singularity of the coefficients. These singularity can be general, not just of pole type.

Keywords: linear differential systems, non-meromorphic coefficients, uniqueness of asymptotic expansions, generalized Stokes sectors.

MSC: Primary 34M03, 34M30; Secondary 34M25, 34M35

Received: 14.01.2025
Revised: 26.01.2025

Language: English

DOI: 10.4213/im9694

 English version: Izvestiya: Mathematics, 2026, 90:1, 87–108