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关于方程f^((k))+A_(k-1)f^((k-1))+…+A_sf^((s))+…+A_1f′+A_0f=0解的增长性 被引量：2

On the growth of the solutions of f^((k))+A_(k-1)f^((k-1))+…+A_sf^((s))+…+A_1f′+A_0f=0
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摘要 研究高阶微分方程f(k)+Ak-1f(k-1)+…+Asf(s)+…+A1f′+A0f=0解的增长性,运用Nevanlinna理论和复域微分方程理论,在一定条件下得到上述方程的每一个非零解都是无穷级,推广并完善了文献[1]的结果。 This paper studies the growth of the solutions off f^（k）＋Ak-1f^（k-1）＋…＋Asf^（s）＋…＋A1f′＋A0f=0 by using the Nevanlinna theory and the complex oscillation theory of differential equations. We obtained the precise estimation of the growth of the solutions of this equation, which generalized and improved the results of Reference [1].
作者 胡梦薇 孙桂荣
机构地区 苏州科技学院数理学院
出处 《苏州科技学院学报（自然科学版）》 CAS 2016年第1期31-35,共5页 Journal of Suzhou University of Science and Technology （Natural Science Edition）
基金 国家自然科学基金资助项目(11001057) 江苏省自然科学基金资助项目(BK2010234)
关键词 增长级 线性微分方程 整函数 order of the growth linear differential equations entire function
分类号 O174.5 [理学—基础数学]
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参考文献11

  • 1吴秀碧,伍鹏程.关于方程f″+Af′+Bf=0解的增长性,其中系数A是一个二阶线性微分方程的解[J].数学物理学报（A辑）,2013,33(1):46-52. 被引量：6
  • 2HAYMAN W K. Meromorphic Functions[M}. Oxford :Clarendon Press, 1964.
  • 3YANG Lo. Value Distribution Theory[M]. Berlin : Spring-Verlag ; Beijing: Science Press, 1993.
  • 4BANK S B ,LAINE I ,LANGLEY J. On the frequency of zeros of solutions of second order linear differential equations[J]. Results Math, 1986, 10:8-24.
  • 5FUCHS W H J. Topics in Nevanlinna Theory[M]. Washington, DC:Naval Research Laboratory, 1970:1-32.
  • 6GUNDEONDONRSEN G G. Finite order solution of second order linear differential equations[J]. Trans Amer Math Soc, 1988,305:415-429.
  • 7STRODT W. Contributions to the asymptotic theory of ordinary differential equations in the complex domain[J]. Mere Amer Math Soc, 1954,13 : 22-34.
  • 8HILLE E. Lectures on Ordinary Differential Equations[M]. California,London,Don Mills,Ontario:Addison-Wesley Publiching Company,Reading Massachusetts-Menlo Park, 1969.
  • 9GUNDERSEN G G. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates[J]. J London Math Soc, 1988,37:88- 104.
  • 10LAINE I,YANG R H. Finite order solutions of complex linear differential equations[J]. Electronic Journal of Differential Equations,2004,65: 1-8.

二级参考文献15

  • 1Bank S B. A note on the zeros of solutions of w1 + P(z)w = 0 where P is a polynomial. Appl Anal, 1987, 25:29-41.
  • 2Bank S B, Laine I. On the oscillation theory of f Af = 0 where A is entire. Trans Amer Math Soc, 1982, 273:351-363.
  • 3Bank S B, Laine I, Langley J. On the frequency of zeros of solutions of secoond order linear differential equations. Results Math, 1986, 10:8- 24.
  • 4Fuchs W H J. Topics in Nevanlinna Theory. Proceedings of the NRL Conference on Classical Function Theory. Washington, DC: Naval Research Laboratory, 1970:1-32.
  • 5Guncersen G G. On the real zeros of solutions of f + A(z)f = 0 where A(z) is entire. Ann Acad Sci Fenn Math, 1986, 11:275-294.
  • 6Gundersen G G. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J London Math Soc, 1988, 37:88- 104.
  • 7Gundersen G G. Finite order solution of second order linear differential equations. Trans Amer Math Soc, 1988, 305:415-429.
  • 8Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964 Hellerstein S, Rossi J. On the distribution of zeros of solutions of second-order differential equations. Complex Variables Theory Appl, 1989, 13:99-109.
  • 9Hellerstein S, Miles J, Rossi J. On the growth of solutions of certain linear differential equations. Ann Acad Sci Fenn (Ser A I Math), 1992, 17:343-365.
  • 10Hille E. Lectures on Ordinary Differntial Equations. California, London, Don Mills, Ontario: Addison- Wesley Publiching Company, Reading, Massachusetts-Menlo Park, 1969.

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苏州科技学院学报（自然科学版）
2016年 第1期

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