一类亚纯函数系数微分方程的复振荡

数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1426-1434.

一类亚纯函数系数微分方程的复振荡

孙桂荣

苏州科技学院数理学院数学系江苏苏州 215009

收稿日期:2013-12-09 修回日期:2014-10-18 出版日期:2014-12-25 发布日期:2014-12-25
基金资助:
国家自然科学基金(11001057)和江苏省自然科学基金(BK2010234)资助.

Oscillation Theory of Solution of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficient

SUN Gui-Rong

Department of Mathematics, University of Science and Technology of Suzhou, Jiangsu Suzhou 215009

Received:2013-12-09 Revised:2014-10-18 Online:2014-12-25 Published:2014-12-25
Supported by:
国家自然科学基金(11001057)和江苏省自然科学基金(BK2010234)资助.

摘要/Abstract

摘要：

研究了系数函数是有限个极点的亚纯函数的高阶慢增长系数线性微分方程, 得到了当方程系数受到很小的扰动时其解的复振荡的一个结果. 推广了Alotaibi等作者的结果.

关键词: 线性微分方程, 零点收敛指数, 有限个极点

Abstract:

This article is devoted to studying the higher order linear differential equations f^(k)+A_k_-2f^(k-2)+…+A₁f'+A₀f=0, where A_j(z)~(j=0,1, …, k-2) are meromorphic functions with at most finitely many poles. We show that small perturbations of such equations lead to solutions whose zeros must have infinite exponent of convergence. Extends some results of Alotaibi etc.

Key words: Linear differential equation, Exponent of convergence of zero-sequence, Meromorphic funtion, Finite poles

中图分类号:

34M10

孙桂荣. 一类亚纯函数系数微分方程的复振荡[J]. 数学物理学报, 2014, 34(6): 1426-1434.

SUN Gui-Rong. Oscillation Theory of Solution of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficient[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1426-1434.

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