华东师范大学学报（自然科学版） >

2019 , Vol. 2019 >Issue 2: 49 - 55

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.02.005

数学

关于二阶线性复微分方程解的Borel方向

  • 魏文龙 ,
  • 黄志刚
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  • 苏州科技大学 数理学院, 江苏 苏州 215000
魏文龙,男,硕士研究生,研究方向为复分析.E-mail:1124177271@qq.com.

收稿日期: 2018-01-13

  网络出版日期: 2019-03-27

基金资助

国家自然科学基金（11001157）；江苏省自然科学基金（BK2010234）；苏州科技大学研究生科研创新计划项目（SKYCX16-007）

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Borel directions of solutions of a second order linear complex differential equation

  • WEI Wen-long ,
  • HUANG Zhi-gang
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  • School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215000, China

Received date: 2018-01-13

  Online published: 2019-03-27

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摘要

利用亚纯函数的Nevanlinna值分布理论，研究了二阶线性复微分方程f"+A（z）f'+B（z）f=0的解的Borel方向，其中A（z）是满足杨不等式极端情况的整函数.证明了当B（z）满足适当条件时，方程的每一个非平凡解为无穷级，并且计算了方程解的Borel方向的个数.

关键词： 无穷级; Borel方向; 杨不等式; Fabry缺项级数; Baker游荡域

本文引用格式

魏文龙 , 黄志刚 . 关于二阶线性复微分方程解的Borel方向[J]. 华东师范大学学报（自然科学版）, 2019 , 2019(2) : 49 -55 . DOI: 10.3969/j.issn.1000-5641.2019.02.005

Abstract

In this paper, we consider the Borel directions of solutions of the differential equation f" + A(z)f' +B(z)f=0. By using Nevanlinna's value distribution theory and assuming that A(z) is extremal for Yang's inequality, we provide conditions for B(z) that guarantee that every non-trivial solution f of the equation is of infinite order; we also calculate the number of Borel directions of these solutions.

Key words： infinite order; Borel directions; Yang's inequality; Fabry gap series; Baker wandering domain

参考文献

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