| 高阶线性微分方程亚纯解的增长性 |
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| 引用本文： | 曾娟娟,刘慧芳. 高阶线性微分方程亚纯解的增长性[J]. 江西师范大学学报(自然科学版), 2016, 40(3): 272-275 |
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| 作者姓名： | 曾娟娟 刘慧芳 |
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| 作者单位： | 江西师范大学数学与信息科学学院,江西 南昌 330022 |
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| 摘 要： | 利用亚纯函数值分布理论,研究了亚纯系数高阶线性微分方程f(k)+Ak-1(z)f(k-1)+…+A0(z)f=0解的增长性,证明了如果A0(z)以∞为亏值,Aj(z)(1≤j≤k-1)满足某些条件,则上述方程的每个非零亚纯解都为无穷级,得到解的超级的下界估计.
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| 关 键 词： | 微分方程 亚纯函数 亏值 级 超级 |
On the Growth of Meromorphic Solutions of Higher Order Linear Differential Equations |
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| ZENG Juanjuan,LIU Huifang. On the Growth of Meromorphic Solutions of Higher Order Linear Differential Equations[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2016, 40(3): 272-275 |
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| Authors: | ZENG Juanjuan LIU Huifang |
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| Affiliation: | College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China |
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| Abstract: | The growth of solutions of higher order linear differential equations f(k)+Ak-1(z)f(k-1)+…+A0(z)f=0 is investigated by using the value distributions theory of meromorphic functions,where Aj(z)(0≤j≤k-1) are meromorphic functions.It is shown that every nonzero meromorphic solution of such equations has infinite order,provided that A0(z) has a deficient value ∞ and Aj(z)(1≤j≤k-1) satisfying certain conditions.The lower bound of hyper order of meromorphic solutions of such equations is also estimated. |
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| Keywords: | differential equation meromorphic functions deficient value order hyper order |
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