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

Michael Gil’

doi:10.3336/gm.50.1.10

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

Michael Gil’

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the equation u′′ = P(z)u, where P(z) is a polynomial. Let z_k(u), k = 1, 2, . . . be the zeros of a solution u(z) to that equation. Inequalities for the sums (formula percent) (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.

Original language	English
Pages (from-to)	183-192
Number of pages	10
Journal	Glasnik Matematicki
Volume	50
Issue number	1
DOIs	https://doi.org/10.3336/gm.50.1.10
State	Published - 1 Jun 2015

Keywords

Bounds for zeros of solutions
Linear differential equation in the complex plane

ASJC Scopus subject areas

General Mathematics

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10.3336/gm.50.1.10

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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 (formula percent) (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.",

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AB - 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 (formula percent) (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.

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KW - Linear differential equation in the complex plane

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

Abstract

Keywords

ASJC Scopus subject areas

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