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Original scientific paper

https://doi.org/10.3336/gm.50.1.10

Sums of zeros of solutions to second order differential equations with polynomial coefficients

Michael Gil' orcid id orcid.org/0000-0002-6404-9618 ; Department of Mathematics , Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel


Full text: english pdf 133 Kb

page 183-192

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Abstract

We consider the equation u''=P(z)u, where P(z) is a polynomial. Let zk(u), k=1, 2, ... be the zeros of a solution u(z) to that equation. Inequalities for the sums ∑k=1j |zk(u)|-1 (j=1, 2, ...) are derived. They considerably improve the previous result of the author. Some applications of the obtained bounds are also discussed. An illustrative example is presented. It shows that the suggested results are sharp.

Keywords

Linear differential equation in the complex plane; bounds for zeros of solutions

Hrčak ID:

140092

URI

https://hrcak.srce.hr/140092

Publication date:

15.6.2015.

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