文章基本信息

标题：On hyper-order of solutions of higher order linear differential equations with meromorphic coefficients
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作者：Jianren Long ; Jun Zhu
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：107
DOI：10.1186/s13662-016-0806-6
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the growth of meromorphic solutions of the differential equations f ( k ) + A k − 1 ( z ) f ( k − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = 0 $$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_)(z)f'+A_((z)f=0 $$ and f ( k ) + A k − 1 ( z ) f ( k − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = F ( z ) , $$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_)(z)f'+A_((z)f=F(z), $$ where A 0 ( z ) ≢ 0 , A 1 ( z ) , … , A k − 1 ( z ) $A_((z)\not\equiv0, A_)(z), \ldots, A_{k-1}(z)$ and F ( z ) ≢ 0 $F(z)\not \equiv0$ are meromorphic functions. A precise estimation of the hyper-order of meromorphic solutions of the above equations is given provided that there exists one dominant coefficient, which improves and extends previous results given by Belaïdi, Chen, etc.
关键词：complex differential equation ; meromorphic function ; hyper-order