奇异点附近的复微分方程解的增长性与系数下级的关系

doi:10.13371/j.cnki.chin.q.j.m.2020.02.003

数学季刊 ›› 2020, Vol. 35 ›› Issue (2): 163-170.doi: 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

School of Mathematical Sciences,Guizhou Normal University

收稿日期:2020-02-21 出版日期:2020-06-30 发布日期:2020-11-10
作者简介: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.
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)；

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

School of Mathematical Sciences,Guizhou Normal University

Received:2020-02-21 Online:2020-06-30 Published:2020-11-10
About author: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.
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)；

摘要/Abstract

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

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

中图分类号:

O175

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.

LIU Yuan-zhu, LONG Jian-ren, ZENG San-gui. On Relationship between Lower-order of Coefficients and Growth of Solutions of Complex Differential Equations near a Singular Point[J]. Chinese Quarterly Journal of Mathematics, 2020, 35(2): 163-170.

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奇异点附近的复微分方程解的增长性与系数下级的关系

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

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