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Bounds for Zeros of Solutions of Second Order Differential Equations with Polynomial Coefficients

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Abstract

We consider the equation \({u''=P(z)u\;\;(z\in\mathbb{C})}\) where P(z) is a polynomial. Let z k (u), k = 1, 2,... be the zeros of a solution u(z) to that equation. Bounds for the sums

$$\sum_{k=1}^{j} \frac {1} {|z_k(u)|}\;(j=1, 2, \ldots)$$

are established. Some applications of these bounds are also considered.

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  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel

    M. I. Gil’

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  1. M. I. Gil’
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Gil’, M.I. Bounds for Zeros of Solutions of Second Order Differential Equations with Polynomial Coefficients. Results. Math. 59, 115–124 (2011). https://doi.org/10.1007/s00025-010-0065-x

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  • DOI: https://doi.org/10.1007/s00025-010-0065-x

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