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On the Growth and Fixed Points of Solutions of Second Order Differential Equations with Meromorphic Coefficients 被引量：17

On the Growth and Fixed Points of Solutions of Second Order Differential Equations with Meromorphic Coefficients
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摘要 In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth. In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.
作者 Zong Xuan CHEN Kwang Ho SHON
机构地区 Department of Mathematics Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期753-764,共12页 数学学报（英文版）
基金 the National Natural Science Foundation of China(No.10161006) the Natural Science Foundation of Guangdong Province in China(No.04010360) the Brain Pool Program of the Korean Federation of Science and Technology Societies(No.021-1-9)
关键词 Differential equation Meromorphic function Order of growth Fixed point Differential equation, Meromorphic function, Order of growth, Fixed point
分类号 O175 [理学—基础数学]
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参考文献17

  • 1Yang, L.: Value Distribution Theory and New Research, Science Press, Beiiing, 1982 (in Chinese).
  • 2Hayman, W.: Meromorphic FUnction, Clarendon Press, Oxford, 1964.
  • 3Laine, I.: Nevanlinna Theory and Complex Differential Equations, W. de Gruyter, Berlin, 1993.
  • 4Hille, E.: Ordinary Differential Equations in the Complex Domain, Wiley, New York, 1976.
  • 5Frei, M.: Uber die subnormalen losungen der differentialgleichung w〃+ e^-zw' + (konst.)w = 0. Comment.Math. Helv., 36, 1-8 (1962).
  • 6Ozawa, M.: On a solution of w〃+ e^-zw' + (az + b)w = 0. Kodai Math. J., 3, 295-309 (1980).
  • 7Gundersen, G.: On the question of whether f〃 + e^-zf' + B(z)f = 0 can admit a solution f absolutely unequal to 0 of finiteorder. Proc, R.S.E., 102(A), 9017 (1986).
  • 8Langley, J. K.: On complex oscillation and a problem of Ozawa. Kodai Math. J., 9, 430-439 (1986).
  • 9Amemiya, I., Ozawa, M.: Non-existence of finite order solutions of w" + e^-zw' + Q(z)2 = 0. Hokkaido Math. J., 10, 1-17 (1981).
  • 10Chen, Z. X.: The growth of solutions of f〃+ e^-zf'+ Q(z)f = 0 where the order (Q) = 1. Science in China (Series A), 45(3), 290-300 (2002).

同被引文献37

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二级引证文献36

Acta Mathematica Sinica,English Series
2005年 第4期

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