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

LIU Yuan-zhu, LONG Jian-ren, ZENG San-gui

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

Chinese Quarterly Journal of Mathematics >

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

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

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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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

Cite this article

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

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