On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

XIONG Hui, LIU Hui-fang

doi:10.13371/j.cnki.chin.q.j.m.2016.04.005

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 4: 369 - 378

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.04.005

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

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College of Mathematics and Information Science,Jiangxi Normal University

XIONG Hui(1989-), male, native of Nanchang, Jiangxi, M.S.D., engages in complex analysis;LIU Hui-fang(1973-), female, native of Fengcheng, Jiangxi, a professor of Jiangxi Normal University, Ph.D.,engages in complex analysis.

Received date: 2014-07-08

Online published: 2020-10-30

Supported by

Supported by the National Natural Science Foundation of China(11201195)； Supported by the Natural Science Foundation of Jiangxi Province(20122BAB201012,20132BAB201008)；

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Abstract

In this paper, we investigate the growth of solutions of the differential equations f^（k）+ A_k-1（z）f^（k-1）+ ··· + A₀（z）f = 0, where A_j（z）（j = 0, ···, k-1） are entire functions.When there exists some coefficient A_s（z）（s ∈ {1, ···, k-1}） being a nonzero solution of f’’+P（z）f = 0, where P（z） is a polynomial with degree n（≥ 1） and A₀（z） satisfies σ（A₀） ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.

Key words： entire function; differential equation; growth of order

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XIONG Hui, LIU Hui-fang . On the Growth of Solutions of a Class of Higher Order Linear Differential Equations[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(4) : 369 -378 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.005

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