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一类高阶线性微分方程解的增长级 被引量：2

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations
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摘要 运用Nevanlinna值分布的基本理论和整函数的相关性质,研究了一类高阶齐次线性微分方程解的增长性,在假设其系数均为整函数,且有1个满足杨-张不等式的极端情况的条件下,证明了方程的每1个非零解均具有无穷级. By using the fundamental theory of value distribution of Nevanlinna and the property of entire function, the growth of solutions of the higher order linear differential equations is considered where coefficients are entire function. Assume that one of coefficients is extremal for Yang-Zhang inequality,it was proved that every nontrivial solution of the complex differential equation has infinite order.
作者 钟文波 易才凤
机构地区 江西师范大学数学与信息科学学院
出处 《江西师范大学学报（自然科学版）》 CAS 北大核心 2014年第4期399-402,共4页 Journal of Jiangxi Normal University(Natural Science Edition)
基金 国家自然科学基金(11171170)资助项目
关键词 整函数 杨-张不等式 微分方程 无穷级 entire function Yang-Zhang inequality differential equations infinite order
分类号 O174.52 [理学—基础数学]
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参考文献6

二级参考文献42

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  • 8Hayman, W.: Meromorphic Functions, Clarendon Press, Oxford, 1964.
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  • 10Chinese original, Springer- Verlag, Berlin; Science Press, Beijing, 1993.

共引文献58

同被引文献17

  • 1陈宗煊.The growth of solutions of f"+e^(-z)f' + Q(z)f = 0 where the order (Q) = 1[J].Science China Mathematics,2002,45(3):290-300. 被引量：20
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  • 6Gundersen G G. On the question of whetherf″ + e-zf′ +B(z)f=O can admit a solutionf=0 of finite order [J]. Pro R S E,1986,102A(1/2) :9-17.
  • 7Barry P D. Some theorems related to the cos πp theorem [ J]. Proc London Math Soc, 1970,21 (3) :334-360.
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  • 10WU PengCheng,ZHU Jun.On the growth of solutions to the complex differential equation f''+Af'+Bf=0[J].Science China Mathematics,2011,54(5):939-947. 被引量：23

引证文献2

二级引证文献5

江西师范大学学报（自然科学版）
2014年 第4期

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