Localization and perturbation of complex zeros of solutions to second order differential equations with polynomial coefficients. A survey
type: Item
instance of: scholarly article
title: Localization and perturbation of complex zeros of solutions to second order differential equations with polynomial coefficients. A survey
zbMATH Open document ID: 1487.34167
DOI: 10.1007/978-3-030-72563-1_8
publication date: 2021-09-07T00:00:00Z
review text: In the main results of this paper the author derives estimates for the sums and products of the zeros of solutions to linear homogeneous second order ordinary differential equations with polynomial coefficients. These estimates are bounds for the function counting the zeros of solutions and information about the zero-free domain. Some other applications of the obtained estimates for the sums and products of the zeros are also discussed. In addition, the author investigates the variation of the zeros of solutions under perturbations of the coefficients. Illustrative examples are also presented. This paper is a survey of the recent results of the author on the complex zeros of solutions to linear homogeneous second order ordinary differential equations with polynomial coefficients, and presents some new results. It is of great significance for future research. For the entire collection see [Zbl 1471.34005].
reviewed by: Wenjun Yuan
Mathematics Subject Classification ID: 34M03
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 34M10
Mathematics Subject Classification ID: 34-02
zbMATH DE Number: 7392143
zbMATH Keywords: linear differential equation in complex plane
zbMATH Keywords: zeros of solutions
zbMATH Keywords: bounds for sums and products of zeros
zbMATH Keywords: perturbation of zeros
author: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: 978-3-030-72563-1 8
OpenAlex ID: W3195829426
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description: scientific article; zbMATH DE number 7392143