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某些差分方程的值分布 被引量：2

Value Distribution of Meromorphic Solutions of Some Difference Equations
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摘要 利用Clunie定理的差分模拟,研究了某些高阶差分方程解的增长性,得到了这些差分方程解的零点和不动点的收敛指数的一些结果及其值分布的情况. By utilizing the difference analogue of Clunie Theorms, the growth of some higher oder difference equa- tions is studied, and some results on the exponent of convergence of zeros, fixed points and value distribution of so- lutions of difference equation are attained.
作者 蒋业阳 陈宗煊
机构地区 华南师范大学数学科学学院
出处 《华南师范大学学报（自然科学版）》 CAS 北大核心 2013年第1期19-23,共5页 Journal of South China Normal University(Natural Science Edition)
基金 国家自然科学基金项目(11171119) 国家自然科学基金数学天元基金项目(11226090) 广东省自然科学基金博士启动基金(S2012040006865)
关键词 差分方程 不动点收敛指数 零点收敛指数 difference equation the exponent of convergence of fixed points the exponent of convergence of zero- sequence
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 e-quations[ M].Berlin: Water de Gruyter, 1993.
  • 3ABLOWITZ M,HALBUD R G, HERBST B. On the exten-sion of Painleve property to difference equations [ J ] . Non-linearity,2000,13;889 -905.
  • 4BERGEWEILER W,LANGLEY J K. Zeros of differencesof meromorphic functions [ J ].Math Proc Cambridge Phi-los Soc,2007,142;133 - 147.
  • 5CHEN Z X,SHON K H. On zeros and fixed points ofdifferences of meromorphic functions [ J ].J Math AnalAppl,2008,344:373 -383.
  • 6CHEN Z X, SHON K H. Value distribution of meromor-phic solutions of certain difference Painlev6 equations[J].J Math Anal Appl,2010,364:556 -566.
  • 7CHIANG Y M,FENG S J. On the Nevanlinna characteris-tic off(z + 7)) and difference equations in the complexplane [ J ].Ramanujan J ,2008,16:10 - 129.
  • 8HALBURD R G,KORHONEN R. Difference analogue ofthe lemma on the logarithmic derivative with applicationsto difference equations[ J] . J Math Anal Appl,2006,314;477 -487.
  • 9HALBURD R G,KORHONEN R. Meromorphic solution ofdifference equation, integrability and the discrete Painlev6equations[ J].J Phys A,2007,40;1 -38.
  • 10HALBURD R G,KORHONEN R. Finite - order mero-morphic solutions and the discrete Painlev6 equations[J].Proc Lond Math Soc,2007,94:443 -474.

二级参考文献7

  • 1HAYMAN W K. Meromorphic function [ M ]. Oxford, UK: Oxford Mathematixal Monographs, Clarendon Press, 1964.
  • 2LAINE I. Nevanlinna theory and complex differential equations [ M ]. Berlin, Getmany : W de Gruyter, 1993.
  • 3HALBURD R G, KORHONEN R. Finite order meromor- phic solutions and the discrete Painlev6 equations [ J ]. Proc Lond Math Soc ,2007,94:443 - 474.
  • 4ABLOWITZ M,HALBURD R G,HERBST B. On the ex- tension of Painleve property to difference equations [ J ]. Nonlinear,2000,13 : 889 - 905.
  • 5CHEN Z X, SHON K H. Value distribution of meromor- phic solutions of certain difference Painleve equations [J]. Journal of Mathematical Analysis and Applications, 2010,364:556 - 566.
  • 6HALBURD R G, KORHONEN R J. Differece analogue of the lemma on the logarithmic derevative with applications to differeee equations [ J ]. Journal of Mathematical Analy- sis and Applications,2006,314:477 -487.
  • 7黄志波,李倩.周期系数高阶线性微分方程的次正规解[J].华南师范大学学报（自然科学版）,2010,42(1):5-8. 被引量：1

同被引文献13

  • 1Hayman W K. Meromorphic functions[M] . Oxford: Clarendon Press, 1964.
  • 2Halburd R G, Korhonen RJ. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].Journal of Mathematical Analysis and Applications, 2006,314 ( 2) : 477 - 487 .
  • 3Laine I, Yang C C. Clunie theorems for difference and qdifference polynomials[J].Journal of the London Mathematical Society ,2007, 76( 2) :556 - 566.
  • 4Chen Z X. On properties of meromorphic solutions for some difference equations[J]. Kodai MathematicalJournal, 2011 ,34: 244 -256.
  • 5Chen Z X. Growth and zeros of meromorphic solutiori of some linear difference equations[J] .Journal of Mathematical Analysis and Applications, 2011,373 ( I ): 235 - 241.
  • 6Peng C W, Chen Z X. On a conjecture concerning some nonlinear difference equations[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2013, 36 (2): 221 -227.
  • 7Chiang Y M, Feng SJ. On the Nevanlinna characteristic of f( z + TJ) and difference equations in the complex plane[J]. The RamanujanJournal ,2008, 16( I): 105 - 129.
  • 8Chen Z X. The zero, pole and order of meromorphic solutions of differential equations with meromorphic coefficients[J]. Kodai MathematicalJournal, 1996, 19: 341 -354.
  • 9Gundersen G. Finite order solutions of second order linear . differential equations[J]. Transactions of the American Mathematical Society, 1988,305: 415 -429.
  • 10CHEN ZongXuan.On growth,zeros and poles of meromorphic solutions of linear and nonlinear difference equations[J].Science China Mathematics,2011,54(10):2123-2133. 被引量：30

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华南师范大学学报（自然科学版）
2013年 第1期

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