文章基本信息

标题：On meromorphic solutions of some linear differential equations with entire coefficients being Fabry gap series
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作者：Shun-Zhou Wu ; Xiu-Min Zheng
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：32
DOI：10.1186/s13662-015-0380-3
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the growth and the exponent of convergence of the sequence of φ-points of meromorphic solutions of the linear differential equations A k ( z ) f ( k ) + A k − 1 ( z ) f ( k − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = 0 $$A_{k}(z)f^{(k)}+A_{k-1}(z)f^{(k-1)}+ \cdots+A_)(z)f'+A_((z)f=0 $$ and A k ( z ) f ( k ) + A k − 1 ( z ) f ( k − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = F ( z ) , $$A_{k}(z)f^{(k)}+A_{k-1}(z)f^{(k-1)}+ \cdots+A_)(z)f'+A_((z)f=F(z), $$ with entire coefficients A j ( z ) $A_{j}(z)$ , j = 0 , 1 , … , k $j=0,1,\ldots,k$ and F ( z ) $F(z)$ , where k ≥ 2 $k\geq2$ , A 0 ( z ) A k ( z ) ≢ 0 $A_((z)A_{k}(z)\not\equiv0$ , φ ( z ) $\varphi(z)$ is a meromorphic function of finite order, and there is only one dominant coefficient A k ( z ) $A_{k}(z)$ of the maximal order, which is also a Fabry gap series.
关键词：linear differential equation ; meromorphic solution ; growth ; exponent of convergence ; Fabry gap series