华东师范大学学报(自然科学版) ›› 2015, Vol. 2015 ›› Issue (1): 75-83.doi: 10.3969/j.issn.1000-5641.2015.01.009

• 应用数学与基础数学 • 上一篇    下一篇

关于一类高阶微分方程的复振荡结果

胡梦薇,黄志刚,孙桂荣   

  1. 1. 苏州科技学院 数理学院, 江苏 苏州 215009; 2. 许昌电气职业学院, 河南 许昌 461000
  • 收稿日期:2013-12-01 出版日期:2015-01-25 发布日期:2015-03-29
  • 通讯作者: 胡梦薇, 女, 硕士, 研究方向为复分析. E-mail:mengweihu1121@163.com
  • 基金资助:

    国家自然科学基金(11001057);

    江苏省自然科学基金(BK2010234);

    江苏省青蓝工程, 苏州科技学院研究生科研创新工程项目(SKCX12S_043

An oscillation result for some higher order linear differential equations

 HU  Meng-Wei, HUANG  Zhi-Gang, SUN  Gui-Rong   

  1. 1. Department of Mathematics, University of Science and Technology of Suzhou, Suzhou Jiangsu 215009, China
    2. Xuchang Eelectrical Vocational College, Xuchang Henan 461000, China
  • Received:2013-12-01 Online:2015-01-25 Published:2015-03-29

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摘要： 运用微分方程复振荡理论,研究了系数是整函数的高阶微分方程解的零点分布问题,在对方程的某个系数做小的扰动的情况下,得到了方程的超越解的零点收敛指数都为无穷.

关键词: 复微分方程, 整函数, 增长级, 零点收敛指数

Abstract: The distribution of zeros of solutions of higher order linear differential equations with entire coefficients was investigated by using complex oscillation theory of linear differential equations. It was proved that the exponent of convergence of zeros of every transcendental solution of the equations is infinite if given a small perturbation to one of the coefficients.

Key words: complex differential equations, entire function, growth of order, exponent of convergence of zeros

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