ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this article, the zeros of solutions of differential equation f^（k）（z）＋A（z）f（z） = 0, are studied, where k 2, A（z） = B（e^z）, B（ζ） = g1（1/ζ） ＋ g2（ζ）, g1 and g2 being entire functions with g2 transcendental and σ（g2） not equal to a positive integer or infinity. It is shown that any linearly independ...

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Bibliographic Details
Published inActa mathematica scientia Vol. 30; no. 4; pp. 1291 - 1300
Main Author 肖丽鹏 陈宗煊
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2010
Institute of Mathematics and Informations,Jiangxi Normal University,Nanchang 330022,China%School of Mathematical Science,South China Normal University,Guangzhou 510631,China
Subjects
30D35
34A20
complex oscillation
dependent
Differential equation
F1赛场
linearly
periodic
复振荡理论
整函数
线性微分方程
线性无关
线性相关
Differential equation
periodic
complex oscillation
34A20
30D35
linearly
dependent
linearly dependent
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Summary:In this article, the zeros of solutions of differential equation f^（k）（z）＋A（z）f（z） = 0, are studied, where k 2, A（z） = B（e^z）, B（ζ） = g1（1/ζ） ＋ g2（ζ）, g1 and g2 being entire functions with g2 transcendental and σ（g2） not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, . . . , fk of Eq.（＊） satisfy λe（f1 . . . fk） ≥ σ（g2） under the condition that fj（z） and fj（z＋ 2πi） （j = 1, . . . , k） are linearly dependent.
Bibliography:linearly dependent
Differential equation; periodic; linearly dependent; complex oscillation
Differential equation
O174.52
periodic
complex oscillation
O175.1
42-1227/O
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(10)60125-7