Bull. Korean Math. Soc. 2021; 58(2): 419-431
Online first article September 7, 2020 Printed March 31, 2021
https://doi.org/10.4134/BKMS.b200321
Copyright © The Korean Mathematical Society.
Guowei Zhang
Anyang Normal University
In this paper we discuss the classical problem of finding conditions on the entire coefficients $A(z)$ and $B(z)$ guaranteeing that all nontrivial solutions of $f''+A(z)f'+B(z)f=0$ are of infinite order. We assume $A(z)$ is an entire function of completely regular growth and $B(z)$ satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) $B(z)$ has a dynamical property with a multiply connected Fatou component, (2) $B(z)$ satisfies $T(r,B)\sim \log M(r,B)$ outside a set of finite logarithmic measure, (3) $B(z)$ is extremal for Denjoy's conjecture.
Keywords: Entire function, infinite order, complex differential equation
MSC numbers: 30D35, 34M10, 37F10
Supported by: This work was supported by NSFC(no.11426035), 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)
2021; 58(6): 1495-1506
2013; 50(4): 1209-1219
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