Growth of Solutions of Complex Differential Equations with Solutions of Another Equation as Coefficients

Growth of Solutions of Complex Differential Equations with Solutions of Another Equation as... 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Growth of Solutions of Complex Differential Equations with Solutions of Another Equation as Coefficients

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
D.O.I.
10.1007/s40315-018-0245-3
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jun 5, 2018

References

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