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

Michael Gil'

doi:10.1016/S0252-9602(12)60081-2

Perturbation 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

2 Scopus citations

Abstract

Let P(z) and P ̃(z) be polynomials of the same degree. We consider the equations . u' = . P(. z). u and u ̃''=P ̃(z)u ̃ (z∈) whose solutions are u(z) and u ̃(z), respectively. Let . z _k(u) and zk(u tild;),k=1,2,..., be the zeros of u(z) and u ̃(z), respectively. We derive bounds for the quantity. kinf|1zk(u)-1zj(u ̃)|.

Original language	English
Pages (from-to)	1083-1092
Number of pages	10
Journal	Acta Mathematica Scientia
Volume	32
Issue number	3
DOIs	https://doi.org/10.1016/S0252-9602(12)60081-2
State	Published - 1 May 2012

Keywords

34A30
34C10
Complex differential equation
Perturbation of zeros
Zeros of solutions

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1016/S0252-9602(12)60081-2

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N2 - Let P(z) and P ̃(z) be polynomials of the same degree. We consider the equations . u' = . P(. z). u and u ̃''=P ̃(z)u ̃ (z∈) whose solutions are u(z) and u ̃(z), respectively. Let . z k(u) and zk(u tild;),k=1,2,..., be the zeros of u(z) and u ̃(z), respectively. We derive bounds for the quantity. kinf|1zk(u)-1zj(u ̃)|.

AB - Let P(z) and P ̃(z) be polynomials of the same degree. We consider the equations . u' = . P(. z). u and u ̃''=P ̃(z)u ̃ (z∈) whose solutions are u(z) and u ̃(z), respectively. Let . z k(u) and zk(u tild;),k=1,2,..., be the zeros of u(z) and u ̃(z), respectively. We derive bounds for the quantity. kinf|1zk(u)-1zj(u ̃)|.

KW - 34A30

KW - 34C10

KW - Complex differential equation

KW - Perturbation of zeros

KW - Zeros of solutions

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U2 - 10.1016/S0252-9602(12)60081-2

DO - 10.1016/S0252-9602(12)60081-2

M3 - Article

AN - SCOPUS:84861317134

SN - 0252-9602

VL - 32

SP - 1083

EP - 1092

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 3

ER -

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

Abstract

Keywords

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