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单位圆内二阶线性微分方程的解与小函数的关系 被引量：5

The Relation Between Solutions of Second Order Linear Differential Equations and Small Functions in the Unit Disc
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摘要 讨论了系数是单位圆内解析函数的二阶齐次和非齐次线性微分方程的解及其一阶导数和二阶导数与小函数之间的关系,并得到了它们之间的精确估计. This paper investigates the relation between solutions of second order homogeneous and non-homogeneous linear differential equations whose coefficients are analytic functions in the unit disc and their small functions, and obtain the precise estimate.
作者 甘会林 向子贵
机构地区 广东商学院数学与计算科学学院
出处 《数学的实践与认识》 CSCD 北大核心 2010年第8期191-195,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(10471048) 高等学校博士学科点专项科研基金(20050574002)
关键词 线性微分方程 小函数 收敛指数. linear differential equation small functions convergence exponent
分类号 O241.8 [理学—计算数学]
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参考文献10

二级参考文献47

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共引文献54

同被引文献45

  • 1金瑾.复方程f″+Af=0的解的零点充满圆[J].数学进展,2005,34(5):609-613. 被引量：28
  • 2陈宗煊,孙光镐.一类二阶微分方程的解和小函数的关系[J].数学年刊（A辑）,2006,27(4):431-442. 被引量：29
  • 3HEITTOKANGAS J. On complex differential equations in the unit disc [J]. Ann Acad Sci Fenn Math Diss,2000,122:1-54.
  • 4TSUJI M. Potential theory in modern function theory[M]. New York : Chelsea, 1975.
  • 5HEITTOKANGAS J, KORHONEN R, RATTYA J. Growth estimates for solutions of linear complex differential equations [J]. Ann Acad Sci Femm Math,2004,29:233-246.
  • 6CAO T B, YI H X. On the complex oscillation of second order linear differential equations with analytic coefficients in the unit disc[ J ]. Chin Ann Math,2007,28A(5 ) :719-732.
  • 7CHEN Z X, SHON K H. The growth of solutions of differential equations with coefficients of small growth in the disc [ J ]. J Math Anal Appl,2004 ,297 :285-304.
  • 8CAO T B, YI H X. The growth of linear differential equations with coefficients of iterated order in the unit disc [ J ]. Math Anal Appl,2006 ,319 :279-294.
  • 9金瑾.高阶线性微分方程解与其小函数的关系[J].理论数学,2012,2(3): 156-163.
  • 10Heittokangas J. On complex differential equations in the unit disc [J]. Ann Acad Sci Fenn Math Diss,2000,122: 1-54.

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数学的实践与认识
2010年 第8期

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