关于二阶线性复微分方程解的Borel方向

魏文龙; 黄志刚

doi:10.3969/j.issn.1000-5641.2019.02.005

关于二阶线性复微分方程解的Borel方向

doi: 10.3969/j.issn.1000-5641.2019.02.005

魏文龙,
黄志刚^,

苏州科技大学数理学院, 江苏苏州 215000

基金项目:

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

详细信息

作者简介:
魏文龙, 男, 硕士研究生, 研究方向为复分析.E-mail:1124177271@qq.com

通讯作者:
黄志刚, 男, 教授, 研究方向为复分析.E-mail:hzg@mail.usts.edu.cn

中图分类号: O174.52
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- 被引次数: 0
出版历程
- 收稿日期: 2018-01-13
- 刊出日期: 2019-03-25

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

WEI Wen-long,
HUANG Zhi-gang^,

School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215000, China

摘要

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.
- 无穷级 /
- Borel方向 /
- 杨不等式 /
- Fabry缺项级数 /
- Baker游荡域
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.
- infinite order /
- Borel directions /
- Yang's inequality /
- Fabry gap series /
- Baker wandering domain

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参考文献(12)

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