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February 11, 2026Izvestiya Mathematics0 citations

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

DGDavide Guzzetti

Key Points

  • The central aim is to establish sufficient conditions for the existence and uniqueness of solutions for a subset of linear ODEs.
  • Reviewed a wide class of ordinary differential equations (ODEs)
  • Analyzed asymptotic behavior of solutions
  • Considered isolated singularities of coefficients
  • Defined conditions for existence and uniqueness of fundamental solutions
  • Identified sufficient conditions that ensure a unique set of solutions
  • Demonstrated that singularities can be of general, not just pole type
  • Concluded that specified asymptotic behavior is achievable within wide sectors

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.

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Cite This Study

Davide Guzzetti (2026) studied this question.

synapsesocial.com/papers/698c1cb3267fb587c655f489https://doi.org/10.4213/im9694e
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