数学季刊 >

2020 , Vol. 35 >Issue 2: 163 - 170

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.02.003

奇异点附近的复微分方程解的增长性与系数下级的关系

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  • School of Mathematical Sciences,Guizhou Normal University
Liu Yuan-zhu(1995-), female, native of Qinglong, Guizhou, a master of Guizhou Normal University, engages in complex analysis; Long Jian-ren(1981-), male, native of Jinping, Guizhou, Professor of Guizhou Normal University, Ph.D supervisor, Ph.D, engages in complex analysis; Zeng San-gui(1993-), male, native of Qianxi, Guizhou, a master of Guizhou Normal University, engages in complex analysis. Corresponding author: Long Jianren.

收稿日期: 2020-02-21

  网络出版日期: 2020-11-10

基金资助

Supported by National Natural Science Foundation of China(11861023)； the Foundation of Science and Technology project of Guizhou Province of China (20185769-05)；

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On Relationship between Lower-order of Coefficients and Growth of Solutions of Complex Differential Equations near a Singular Point

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  • School of Mathematical Sciences,Guizhou Normal University
Liu Yuan-zhu(1995-), female, native of Qinglong, Guizhou, a master of Guizhou Normal University, engages in complex analysis; Long Jian-ren(1981-), male, native of Jinping, Guizhou, Professor of Guizhou Normal University, Ph.D supervisor, Ph.D, engages in complex analysis; Zeng San-gui(1993-), male, native of Qianxi, Guizhou, a master of Guizhou Normal University, engages in complex analysis. Corresponding author: Long Jianren.

Received date: 2020-02-21

  Online published: 2020-11-10

Supported by

Supported by National Natural Science Foundation of China(11861023)； the Foundation of Science and Technology project of Guizhou Province of China (20185769-05)；

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摘要

We investigate the growth of solutions of the following complex linear differential equation f’’+ A（z）f’+ B（z）f = 0,where A（z） and B（z） are analytic functions in C-{z0}, z0 ∈ C. Some estimations of lower bounded of growth of solutions of the differential equation are obtained by using the concept of lower order. 

关键词： Complex differential equation; Lower-order of growth; Lower-type; Analytic function; Near a singular point

本文引用格式

刘元竹, 龙见仁, 曾三桂 . 奇异点附近的复微分方程解的增长性与系数下级的关系[J]. 数学季刊, 2020 , 35(2) : 163 -170 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.003

Abstract

We investigate the growth of solutions of the following complex linear differential equation f’’+ A（z）f’+ B（z）f = 0,where A（z） and B（z） are analytic functions in C-{z0}, z0 ∈ C. Some estimations of lower bounded of growth of solutions of the differential equation are obtained by using the concept of lower order. 

Key words： Complex differential equation; Lower-order of growth; Lower-type; Analytic function; Near a singular point

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