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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.

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

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  • Received Date: March 02, 2016
  • Revised Date: April 22, 2016
  • By utilizing the difference analogue of Nevanlinna's value distribution theory of meromorphic functions, the order of growth of meromorphic solutions of certain difference Painlevˊe equation I and difference Painlevˊe equation II is investigated and some important results are obtained. The accurate estimate of the order of growth of meromorphic solutions to certain difference Painlevˊe equation I and difference Painlevˊe equation II is attained under the given conditions.
  • [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+η) 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+η) and difference equations in the complex plane[J]. Ramanujan J., 2008, 16(1): 105-129.

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