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August 2006 On the growth of solutions of $w^{\left( n\right)}+e^{-z}w^{^{\prime }}+Q\left( z\right) w=0$ and some related extensions
Saade HAMOUDA, Benharrat BELA\"IDI
Hokkaido Math. J. 35(3): 573-586 (August 2006). DOI: 10.14492/hokmj/1285766417

Abstract

In this paper, we show that if $Q\left( z\right) $ is a nonconstant polynomial, then every solution $w\not\equiv 0$ of the differential equation $w^{\left( n\right) }+e^{-z}w^{^{\prime }}+Q\left( z\right) w=0,$ has infinite order and we give an extension of this result. We will also show that if the equation $w^{\left( n\right) }+e^{-z}w^{^{\prime }}+cw=0$, where $c\neq 0$ is a complex constant, possesses a solution $w\not\equiv 0$ of finite order, then $c=-k^{n}$ where $% k$ is a positive integer. In the end, by study more general, we investigate the problem when $\sigma \left( Q\right) =1.$

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Saade HAMOUDA. Benharrat BELA\"IDI. "On the growth of solutions of $w^{\left( n\right)}+e^{-z}w^{^{\prime }}+Q\left( z\right) w=0$ and some related extensions." Hokkaido Math. J. 35 (3) 573 - 586, August 2006. https://doi.org/10.14492/hokmj/1285766417

Information

Published: August 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1131.34058
MathSciNet: MR2275502
Digital Object Identifier: 10.14492/hokmj/1285766417

Subjects:
Primary: 34M10
Secondary: 30D35

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 3 • August 2006
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