Comput. Methods Funct. Theory https://doi.org/10.1007/s40315-018-0245-3 Growth of Solutions of Complex Differential Equations with Solutions of Another Equation as Coefﬁcients 1 1 1 Jianren Long · Tingmi Wu · Xiubi Wu Received: 21 November 2017 / Revised: 22 February 2018 / Accepted: 1 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We study the growth of solutions of f + A(z) f + B(z) f = 0, where A(z) and B(z) are non-trivial solutions of another second-order complex differential equations. Some conditions guaranteeing that every non-trivial solution of the equation is of inﬁnite order are obtained, in which the notion of accumulation rays of the zero sequence of entire functions is used. Keywords Complex differential equation · Entire function · Inﬁnite order · Asymptotic growth Mathematics Subject Classiﬁcation Primary 34M10; Secondary 30D35 1 Introduction and Main Results Yosida was among the ﬁrst who applied Nevanlinna theory of meromorphic functions to complex differential equations, see [34]; complex differential equations have been an active research ﬁeld since then. In this paper, the growth of solutions of complex Communicated by Risto Korhonen. B Jianren Long longjianren2004@163.com; jrlong@gznu.edu.cn Tingmi Wu 1849565458@qq.com Xiubi Wu basicmath@163.com School of Mathematical Sciences, Guizhou Normal
Computational Methods and Function Theory – Springer Journals
Published: Jun 5, 2018
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