Sums of zeros of solutions to non-homogeneous ODE with polynomial coefficients

Michael Gil

doi:10.1016/j.jmaa.2014.06.045

Sums of zeros of solutions to non-homogeneous ODE with polynomial coefficients

Michael Gil

Department of Mathematics

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

3 Scopus citations

Abstract

We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let z_k(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

Original language	English
Pages (from-to)	1917-1924
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	421
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.06.045
State	Published - 1 Jan 2015

Keywords

ODE in the complex plane
Zeros of solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2014.06.045

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abstract = "We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.",

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N2 - We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

AB - We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

KW - ODE in the complex plane

KW - Zeros of solutions

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VL - 421

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Sums of zeros of solutions to non-homogeneous ODE with polynomial coefficients

Abstract

Keywords

ASJC Scopus subject areas

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