文章基本信息

标题：On the growth of solutions of certain higher-order linear differential equations
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作者：Zhiqiang Mao ; Huifang Liu
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：33
DOI：10.1186/1687-1847-2014-33
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the growth of meromorphic solutions of the 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 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = F ( z ) , where A 0 ( z ) (≢0), A 1 ( z ) , … , A k − 1 ( z ) and F ( z ) (≢0) are entire functions of finite order. We find some conditions on the coefficients to guarantee that every nontrivial meromorphic solution of such equations is of infinite order. MSC:30D35, 34M10.
关键词：entire function ; differential equation ; order