Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

doi:10.1007/s42967-022-00219-9

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4): 1524-1533.doi: 10.1007/s42967-022-00219-9

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Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

Michael Gil'

The Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

收稿日期:2021-10-18 修回日期:2022-09-08 发布日期:2023-12-16
通讯作者: Michael Gil',E-mail:gilmi@bezeqint.net E-mail:gilmi@bezeqint.net

Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

Michael Gil'

The Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Received:2021-10-18 Revised:2022-09-08 Published:2023-12-16
Contact: Michael Gil',E-mail:gilmi@bezeqint.net E-mail:gilmi@bezeqint.net

摘要/Abstract

摘要： The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients. We derive estimates for the partial sums and products of the zeros of solutions to the considered equations. These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.

关键词: Ordinary differential equations, Linear equations, Zeros of solutions

Abstract: The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients. We derive estimates for the partial sums and products of the zeros of solutions to the considered equations. These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.

Key words: Ordinary differential equations, Linear equations, Zeros of solutions

中图分类号:

34C10
34A30

Michael Gil'. Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts[J]. Communications on Applied Mathematics and Computation, 2023, 5(4): 1524-1533.

参考文献

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Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

Inequalities for Sums and Products of Complex Zeros of Solutions to ODE with Polynomial Right Parts

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