数学物理学报 ›› 2013, Vol. 33 ›› Issue (3): 401-408.

• 论文 •    下一篇

一类高阶线性微分方程解的增长性

龙见仁1,2|朱军3|李晓曼1   

  1. 1.贵州师范大学 数学与计算机科学学院 贵阳 550001|
    2.中国科学院数学与系统科学研究院 北京 100190|3.北京大学 数学科学学院 北京 100871
  • 收稿日期:2011-05-24 修回日期:2012-10-20 出版日期:2013-06-25 发布日期:2013-06-25
  • 基金资助:

    国家自然科学基金(11171080)和贵州省科学技术基金(黔科合J字LKS[2010]07)资助

On the Growth of Solutions of Some Higher Order Linear Differential Equations

 LONG Jian-Ren1,2, ZHU Jun3, LI Xiao-Man1   

  1. 1.School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001;
    2.Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing |100190;
    3.School of Mathematical Sciences, Peking University, Beijing |100871
  • Received:2011-05-24 Revised:2012-10-20 Online:2013-06-25 Published:2013-06-25
  • Supported by:

    国家自然科学基金(11171080)和贵州省科学技术基金(黔科合J字LKS[2010]07)资助

摘要:

利用亏值研究了下列高阶线性微分方程解的增长性
f (k)+Ak-1(z)f(k-1)+…+A1(z)f' +A0(z)f=0,
其中Aj(z) (j=0, 1, …, k-1)是整函数, 并且获得了一些比先前更广泛的结果.更进一步, 如果方程的解f(≠0)为无穷级时, 获得了f 的超级的下界估计.

关键词: 复微分方程, 整函数, 亏值, 超级

Abstract:

In this paper, we shall involve the deficient value in investigating the growth of  solutions of the linear differential equation f (k)+Ak-1(z)f(k-1)+…+A1(z)f' +A0(z)f=0,
where Aj(z) (j=0, 1, …, k-1) are entire functions, and we obtain some results which improves some earlier results. More specifically, we estimate the lower bounded of hyper-order of solutions of the equation if every solution f(≠0) of the equation is of infinite order.

Key words: Complex differential equations, Entire function, Deficient value, Hyper-order

中图分类号: 

  • 34M10