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某些q-差分方程亚纯解的增长性 被引量：1

Growth of Meromorphic Solutions of Some q-Difference Equations
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摘要 运用Nevanlinna理论的基本方法研究了某些比Schroder方程更为一般的q-差分方程的亚纯解,当方程系数在给定的条件下对解的增长性进行了估计,推广了前人已有的结果,并给出了一些例子说明这些结果是精确的. By using the fundermental method of Nevanlinna theory, the authors consider meromorphic solutions of some q-difference equations which are more general than the SchrSder equation. Estimates on growth of solutions are given under some conditions on the coefficients of these equations, which generalize the earlier results. Some examples are also given to show that these results are sharp.
作者 郑秀敏 陈宗煊
机构地区 华南师范大学数学科学学院 江西师范大学数学与信息科学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2009年第5期647-658,共12页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.10871076) 广东省自然科学基金(No.06025059)资助的项目
关键词 q-差分方程 Schrder方程 亚纯解 q-Difference equation, SchrSder equation, Meromorphic solution
分类号 O174.52 [理学—基础数学]
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参考文献18

  • 1Hayman W. K., Meromorphic Functions [M], Oxford: Clarendon Press, 1964.
  • 2Laine I., Nevanlinna Theory and Complex Differential Equations [M], Berlin: Walter de Gruyter, 1993.
  • 3Nevanlinna R., Analytic Function [M], Berlin, New York, Heidelberg: Springer-Verlag, 1970.
  • 4Yang L., Value Distrbution Theory [M], Berlin: Springer-Verlag; Beijing: Science Press, 1993.
  • 5Ablowitz M. J., Halbrud R. G. and Herbst B., On the extension of the Painleve property to difference equations [J], Nonlinearity, 2000, 13:889-905.
  • 6Bergweiler W. and Langley J. K., Zeros of differences of meromorphic functions [J], Math. Proc. Cambridge Philos. Soc., 2007, 142:133-147.
  • 7Chen Z. X. and Shon K. H., On zeros and fixed points of differences of meromorphic functions [J], J. Math. Anal. Appl., 2008, 344(1):373-383.
  • 8Chiang Y. M. and Feng S. J., On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions [J], Trans. Amer. Math. Soc., 2009, 361:3767-3791.
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  • 10Halburd R. G. and Korhonen R. J., Finite-order meromorphic solutions and the discrete Painleve eqations [J]. Proc. London Math. Soc., 2007, 94:443-474.

同被引文献11

  • 1涂金,陈宗煊,郑秀敏.几类高阶微分方程解的复振荡[J].数学杂志,2007,27(1):77-82. 被引量：2
  • 2Hayman W K. Meromorphic functions [M]. Oxford: Clarendon Press, 1964.
  • 3Laine I. Nevanlinna theorey and complex differential equations [M]. Berlin: Walter de Gruyter, 1993.
  • 4Nevanlinna R. Analytic function [M]. Berlin, New York, Heidelberg: Springer-Verlag, 1970.
  • 5Yang Lo. Value distribution theory [M]. Berlin: Springer-Verlag; Beijing: Science Press, 1993.
  • 6Laine I, Rieppo J, Silvennoinen H. Remarks on the complex difference equations[J]. Comput. Meth- ods Funct. Theory, 2005, 5: 77-88.
  • 7Zheng Xiumin, Chen Zongxuan, Tu Jin. Growth of meromorphic solutions of some difference equa- tions[J]. Appl. Anal. Discrete Math, 2010, 4: 309-321.
  • 8Goldstein R. Some results on factorization of meromorphic functions [J]. J. London Math. Soc., 1971, 4(2): 357-364.
  • 9Goldstein R. On meromorphic results of certain functional equations [J]. Aequationes Math., 1978, 18: 112-157.
  • 10Rieppo J. On a class of complex functional equations [J]. Ann. Acad. Sci. Fenn. Math., 2007, 32: 151-170.

引证文献1

数学年刊（A辑）
2009年 第5期

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