Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2021; 58(6): 1495-1506

Published online November 30, 2021 https://doi.org/10.4134/BKMS.b201051

Copyright © The Korean Mathematical Society.

The growth of solutions of complex differential equations with entire coefficient having finite deficient value

Guowei Zhang

Anyang Normal University

Abstract

The growth of solutions of second order complex differential equations $f''+A(z)f'+B(z)f=0$ with transcendental entire coefficients is considered. Assuming that $A(z)$ has a finite deficient value and that $B(z)$ has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

Keywords: Entire function, infinite order, complex differential equation

MSC numbers: 30D35, 34M10, 37F10

Supported by: This work was supported by the key scientific research project for higher education institutions of Henan Province, China (No. 18A110002) and training program for young backbone teachers of colleges and universities in Henan Province, China (No. 2017GGJS126).