International Journal of Differential Equations

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

Michael Gil’

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Abstract

We consider the equation u=P(z)u+F(z)(zC), 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 k=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.

Article information

Source
Int. J. Differ. Equ., Volume 2015 (2015), Article ID 690519, 6 pages.

Dates
Received: 14 July 2015
Revised: 22 October 2015
Accepted: 29 October 2015
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881449

Digital Object Identifier
doi:10.1155/2015/690519

Mathematical Reviews number (MathSciNet)
MR3429206

Zentralblatt MATH identifier
1339.34094

Citation

Gil’, Michael. Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients. Int. J. Differ. Equ. 2015 (2015), Article ID 690519, 6 pages. doi:10.1155/2015/690519. https://projecteuclid.org/euclid.ijde/1484881449


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