Localization and Perturbation of Complex Zeros of Solutions to Second Order Differential Equations with Polynomial Coefficients. A Survey

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Abstract

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. In particular, estimates for the sums and products of the zeros are derived. These estimates give us 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, we investigate the variation of the zeros of solutions under perturbations of the coefficients. Illustrative examples are also presented. A part of the results presented in the paper is new.

Original languageEnglish
Title of host publicationSpringer Optimization and Its Applications
PublisherSpringer
Pages149-186
Number of pages38
DOIs
StatePublished - 1 Jan 2021

Publication series

NameSpringer Optimization and Its Applications
Volume173
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

Keywords

  • Bounds for sums and products of zeros
  • Linear differential equation in the complex plane
  • Perturbation of zeros
  • Zeros of solutions

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