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 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.b200321Published online September 7, 2020Printed 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) Downloads: Full-text PDF   Full-text HTML