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某类差分微分多项式和差分微分方程亚纯解的性质

Properties of Certain Difference-differential Polynomial and Meromorphic Solution of Difference-differential Equation
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摘要 利用亚纯函数差分的Nevanlinna值分布理论,研究了一类平移差分微分多项式的零点分布和一类平移差分微分方程亚纯解的性质,推广和改进了一些文献的结论。 In this paper,using the difference Nevanlinna theory,investigate the Zeros distribution of cer-tain q-shift difference-differential polynomial and properties of meromorphic solution certain q-shift differ-ence-differential equation.Improvements and extensions of some results in references are presented.
作者 樊艺
机构地区 毕节学院理学院
出处 《毕节学院学报（综合版）》 2014年第8期18-23,共6页 Journal of Bijie University
基金 贵州省科学技术基金资助项目"复微分方程解的理论研究"成果之一 项目编号:2012GZ10526
关键词 差分微分多项式 亚纯解 零级 零点 Difference-differential Polynomial Meromorphic Solution Zero-order Zeros
分类号 O174.52 [理学—基础数学]
  • 相关文献

参考文献14

  • 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 functions[M].Berlin : Springer-Verlag, 1970.
  • 4Yang C C,Yi H X.Uniqueness Theory of Meromorphic functions[M].Dordrecht: Kluwer Academic Publish-ers Group,2003.
  • 5Halburd R G, Korhonen R J. Meromorphic solutions of difference equations, integrability and the discrete Painlev6 equations[J]. Journal of Physics A: Mathematical and Theoretical, 2007, 40(6): 1-38.
  • 6Halburd R G, Korhonen R J. Difference analogue of the lemma on the logarithmic derivative with applica- tions to difference equations[J]. Journal of Mathematical Analysis and Applications, 2006, 314(2): 477-487.
  • 7Chiang Y M, Feng S J. On the Nevanlinna characteristic of f (z+ "q) and difference equations in the complex plane[J]. The Ramanujan Journal, 2008, 16(1): 105-129.
  • 8Liu K, Qi X G. Meromorphic solutions of q-shift difference equations[J]. Ann. Pol. Math, 2011, 101(3): 215-225.
  • 9涂金,郑秀敏.q-平移差分多项式和推广了的q-平移差分方程亚纯解的一些性质[J].数学物理学报（A辑）,2013,33(5):951-959. 被引量：3
  • 10刘凯,杨连中.关于复差分微分理论的若干结果[J].数学杂志,2013,33(5):830-836. 被引量：4

二级参考文献21

  • 1Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964.
  • 2Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin: Walter de Cruyter, 1993.
  • 3Nevanlinna R. Analytic Functions. Berlin: Springer-Verlag, 1970.
  • 4Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions. Dordrecht: Kluwer Academic Publishers Group, 2003.
  • 5Bergweiler W, Ishizaki K, Yanagihara N. Meromorphic solutions of some fnnctonal equations. Methods Appl Anal, 1998, 5(3): 248-258 (Correction: Methods Appl Anal, 1999, 6(4): 617 618).
  • 6Bergweiler W, Langley J K. Zeros of differences of meromorphic functions. Math Proc Cambridge Phil Soc, 2007, 142:133-147.
  • 7Chen Z X, Huang Z B, Zheng X M. On properties of difference polynomials. Acta Math Scientia, 2011, 31B(2): 627-633.
  • 8Chiang Y M, Feng S J. On the nevanlinna characteristic of f(z+rl) and difference equations in the complex plane. Ramanujan J, 2008, 16:105-129.
  • 9Halburd R G, Korhonen R J. Difference analogue of the lemma on the logarithmic derivative with appli- cations to difference equations. J Math Anal Appl, 2006, 314:477-487.
  • 10Halburd R G, Korhonen R J. Meromorphic solutions of difference equations, integrability and the discrete painlev6 equations. J Phys A, 2007, 40:1-38.

共引文献5

毕节学院学报（综合版）
2014年 第8期

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