The infinite growth of solutions of second order linear complex differential equations with completely regular growth coefficient
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 419-431
https://doi.org/10.4134/BKMS.b200321
Published online September 7, 2020
Printed March 31, 2021
Guowei Zhang
Anyang Normal University
Abstract : 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)
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