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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 被引量：3

Some Properties of q-Shift Difference Polynomials and Meromrophic Solutions of Generalized q-Shift Difference Equations
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摘要 研究了某些推广了的q-平移差分方程亚纯解的增长性.还研究了q-平移差分多项式的值分布,这些结果可以视为复微分多项式对应结果的q-平移差分模拟.亦给出了一些例子说明所得结果的精确性. In this paper,we investigate the growth of meromorphic solutions of some generalized q-shift difference equations.We also investigate the value distribution of q-shift difference polynomials,which can be viewed as q-shift difference analogues of corresponding results of differential polynomials.Examples are also given to illustrate the sharpness of our results.
作者 涂金 郑秀敏
机构地区 江西师范大学数学与信息科学学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2013年第5期951-959,共9页 Acta Mathematica Scientia
基金 国家自然科学基金(11126145 11171119) 江西省自然科学基金(20114BAB211003 20122BAB211005)资助
关键词 q-平移差分方程 q-平移差分多项式 亚纯解 零级 q-Shift difference equation q-Shift difference polynomials Meromorphic solution Zero-order
分类号 O174.52 [理学—基础数学]
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参考文献19

  • 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.
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  • 10Halburd R G, Korhonen R J. Meromorphic solutions of difference equations, integrability and the discrete painlev6 equations. J Phys A, 2007, 40:1-38.

同被引文献15

  • 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.
  • 9Barnett D C, Halburd R G, Morgan W, et al. Nevanlinna theory for q-difference operator and meromorphic solutions of q-difference equations[J]. PROCEEDINGS-ROYAL SOCIETY OF EDINBURGH A, 2007, 137 (3): 457-474.
  • 10Zhang J, Korhonen R. On the Nevanlinna characteristic of f (qz) and its applications[J]. Journal of Mathe- matical Analysis and Applications, 2010, 369(2): 537-544.

引证文献3

数学物理学报（A辑）
2013年 第5期

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