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

Michael Gil’ ()
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Michael Gil’: Ben Gurion University of the Negev

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 149-186 from Springer

Abstract: 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.

Keywords: Linear differential equation in the complex plane; Zeros of solutions; Bounds for sums and products of zeros; Perturbation of zeros; 34C10; 34A30 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_8

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DOI: 10.1007/978-3-030-72563-1_8

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