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差分Painleve方程亚纯解的增长级

彭长文

彭长文. 差分Painleve方程亚纯解的增长级[J]. 华南师范大学学报(自然科学版), 2018, 50(1): 102-105.
引用本文: 彭长文. 差分Painleve方程亚纯解的增长级[J]. 华南师范大学学报(自然科学版), 2018, 50(1): 102-105.
The Order of Growth of Meromorphic Solutions for Some Difference Painleve Equations[J]. Journal of South China normal University (Natural Science Edition), 2018, 50(1): 102-105.
Citation: The Order of Growth of Meromorphic Solutions for Some Difference Painleve Equations[J]. Journal of South China normal University (Natural Science Edition), 2018, 50(1): 102-105.

差分Painleve方程亚纯解的增长级

基金项目: 

贵州省科技厅项目;贵州省教育厅项目;贵州省教育厅项目

详细信息
    通讯作者:

    彭长文

The Order of Growth of Meromorphic Solutions for Some Difference Painleve Equations

  • 摘要: 利用亚纯函数的Nevanlinna值分布理论的差分模拟,研究了给定的差分Painlev$\acute{e}$方程I和差分Painlev$\acute{e}$方程II的超越亚纯解的增长性,得到了一些有意义的结果:在给定的条件下,给出了给定的差分Painlev$\acute{e}$方程I和差分Painlev$\acute{e}$方程II的超越亚纯解的增长级的精确估计.
  • [1] HAYMAN W K. Meromorphic functions[M]. Oxford: Clarendon Press, 1964.
    [2] ABLOWITZ M, HALBURD R G, HERBST B. On the extention of Painlev′e property to difference equations[J]. Nonlinearity, 2000,13(1): 889–905.
    [3] HALBURD R G, KORHONEN R J. Existence of finite-order meromorphic solutions as a detector of integrability of difference equations[J]. J. Phys., 2006, D(218): 191–203.
    [4] HALBURD R G, KORHONEN R J. Meromorphic solution of difference equation, integrability and the discrete Painlev′e equations[J]. J. Phys., 2007, A(40): 1–38.
    [5] HALBURD R G, KORHONEN R J. Finite-order meromorphic solutions and the discrete Painlev′e equations[J]. Proc. Lond. Math. Soc., 2007, 94(6): 443–474.
    [6] CHEN Z X, SHON K H. Value distribution of meromorphic solutions of certain difference Painlev′e equations[J]. J. Math. Anal. Appl., 2010, 364(1): 556–566.
    [7] CHEN M R, CHEN Z X. On properties of meromorphic solution of certain difference Painlev′e equation[J]. Bull. Aust. Math. Soc., 2012, 85(3): 463–475.
    [8] CHEN Z X. On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations[J]. Sci. China Math., 2011, 54(8): 2123–2133.
    [9] PENG C W, CHEN Z X. On a conjecture concerning some nonlinear difference equations [J]. Bull. Malays. Math. Sci. Soc., 2013, 36 (2): 221–227.
    [10]陈宗煊,黄志波.复域差分和差分方程的研究[J].华南师范大学学报(自然科学版), 2013, 45 (6): 26-33.
    [11]蒋业阳,陈宗煊.某些差分方程的值分布[J]. 华南师范大学学报(自然科学版), 2013, 45 (1): 19-23.
    [12]CHIANG Y M, FENG S J. On the Nevanlinna characteristic of $f(z + \eta)$ and difference equations in the complex plane[J]. Ramanujan J., 2008, 16(1): 105-129.

    [1] HAYMAN W K. Meromorphic functions[M]. Oxford: Clarendon Press, 1964.
    [2] ABLOWITZ M, HALBURD R G, HERBST B. On the extention of Painlev′e property to difference equations[J]. Nonlinearity, 2000,13(1): 889–905.
    [3] HALBURD R G, KORHONEN R J. Existence of finite-order meromorphic solutions as a detector of integrability of difference equations[J]. J. Phys., 2006, D(218): 191–203.
    [4] HALBURD R G, KORHONEN R J. Meromorphic solution of difference equation, integrability and the discrete Painlev′e equations[J]. J. Phys., 2007, A(40): 1–38.
    [5] HALBURD R G, KORHONEN R J. Finite-order meromorphic solutions and the discrete Painlev′e equations[J]. Proc. Lond. Math. Soc., 2007, 94(6): 443–474.
    [6] CHEN Z X, SHON K H. Value distribution of meromorphic solutions of certain difference Painlev′e equations[J]. J. Math. Anal. Appl., 2010, 364(1): 556–566.
    [7] CHEN M R, CHEN Z X. On properties of meromorphic solution of certain difference Painlev′e equation[J]. Bull. Aust. Math. Soc., 2012, 85(3): 463–475.
    [8] CHEN Z X. On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations[J]. Sci. China Math., 2011, 54(8): 2123–2133.
    [9] PENG C W, CHEN Z X. On a conjecture concerning some nonlinear difference equations [J]. Bull. Malays. Math. Sci. Soc., 2013, 36 (2): 221–227.
    [10]陈宗煊,黄志波.复域差分和差分方程的研究[J].华南师范大学学报(自然科学版), 2013, 45 (6): 26-33.
    [11]蒋业阳,陈宗煊.某些差分方程的值分布[J]. 华南师范大学学报(自然科学版), 2013, 45 (1): 19-23.
    [12]CHIANG Y M, FENG S J. On the Nevanlinna characteristic of $f(z + \eta)$ and difference equations in the complex plane[J]. Ramanujan J., 2008, 16(1): 105-129.
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出版历程
  • 收稿日期:  2016-03-03
  • 修回日期:  2016-04-23
  • 刊出日期:  2018-02-25

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