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

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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.

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Acknowledgements

The authors would like to thank Professor Gary G. Gundersen for valuable suggestions to improve the present article. The authors also would like to thank the referees for valuable comments to improve the present article. This research work is supported by the National Natural Science Foundation of China (Grant no. 11501142), and the Foundation of Science and Technology of Guizhou Province of China (Grant no. [2015]2112), and the Foundation of Doctoral Research Program of Guizhou Normal University 2016, and the Foundation of Qian Ceng Ci Innovative Talents of Guizhou Province 2016.

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  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, People’s Republic of China

    Jianren Long, Tingmi Wu & Xiubi Wu

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  1. Jianren Long
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  2. Tingmi Wu
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Correspondence to Jianren Long.

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Communicated by Risto Korhonen.

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Long, J., Wu, T. & Wu, X. Growth of Solutions of Complex Differential Equations with Solutions of Another Equation as Coefficients. Comput. Methods Funct. Theory 19, 3–16 (2019). https://doi.org/10.1007/s40315-018-0245-3

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  • DOI: https://doi.org/10.1007/s40315-018-0245-3

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