Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

Michael Gil'

doi:10.1155/2015/690519

Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

Michael Gil'

Department of Mathematics

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

2 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. Lower estimates for the products Π_k=1^j | z_k(u) | (j = 1,2,⋯) are derived. In particular, they give us a bound 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
Article number	690519
Journal	International Journal of Differential Equations
Volume	2015
DOIs	https://doi.org/10.1155/2015/690519
State	Published - 1 Jan 2015

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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. Lower estimates for the products Πk=1j | zk(u) | (j = 1,2,⋯) are derived. In particular, they give us a bound 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. Lower estimates for the products Πk=1j | zk(u) | (j = 1,2,⋯) are derived. In particular, they give us a bound 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. Lower estimates for the products Πk=1j | zk(u) | (j = 1,2,⋯) are derived. In particular, they give us a bound 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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ER -

Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

Abstract

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