JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (10): 34-40.doi: 106040/j.issn.16719352.0.2015628

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Meromorphic solutions of a type of system of complex difference equations

LIU Man-li, GAO Ling-yun*   

  1. Department of Mathematics, Jinan University, Guangzhou 510632, Guangdong, China
  • Received:2015-12-21 Online:2016-10-20 Published:2016-10-17

Abstract: The method of Nevanlinna value distribution theory concerning meromorphic functions is used, a problem for the existence of meromorphic solutions on a type of system of complex difference equations and the form about a type of system of complex difference equations are investigated. Under the assumption restricted to certain proper conditions, two results about the type of system of complex difference equations are obtained, and some examples show that the results are precise.

Key words: value distribution theory, difference equations, system of complex difference equations, the growth order, meromorphic solution

CLC Number: 

  • O174.52
[1] 仪洪勋,杨重骏.亚纯函数的唯一性理论[M].北京:科学出版社,1995.
[2] 何育赞,肖修治.常微分方程与代数体函数[M].北京:科学出版社,1998.
[3] LAINE I. Nevanlinna theory and complex differential equations[M].Berlin:Walter de Gruyter, 1993.
[4] YANG C C, LAINE I.On analogies between nonlinear difference and differential equations[J].Proceedings of the Japan Academy(Series A), 2010, 86(1):10-14.
[5] CHIANG Y M, FENG S J. On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane[J].The Ramanujan Journal, 2008, 16(1):105-129.
[6] 高凌云.关于一类复差分方程的亚纯解[J].数学年刊,2014,35A(2):193-202. GAO Lingyun. On meromorphic solutions to a type of complex difference equations[J].Chinese Annals of Mathematics, 2014, 35A(2):193-202.
[7] HALBURD R G, KORHONEN R J. 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.
[8] CHEN Z X, HUANG Z B, ZHANG R R. On difference equations relating to Gamma function[J].Atca Mathematica Scientia, 2011, 31B(4):1281-1294.
[9] 高凌云.复高阶差分方程解[J].数学学报,2013,56(4):451-458. GAO Lingyun. Solutions of complex higher-order difference equations[J].Acta Mathematica Sinica, 2013, 56(4):451-458.
[10] HEITTOKANGAS J, KORHONEN R, LAINE I, et al.Complex difference equations of Malmquist type[J]. Computational Methods and Function Theory, 2001(1):27-39.
[11] KORHONEN R J. A new Clunie type theorem for difference polynomial[J].Journal of Difference Equations and Applications, 2011, 17(3):387-400.
[12] LI Haichou, GAO Lingyun. Meromorphic solutions of a type of system of complex differential-difference equations[J]. Acta Mathematica Scientia, 2015, 35B(1):195-206.
[13] 高凌云.Malmquist型复差分方程组[J].数学学报,2012,55(20):293-300. GAO Lingyun. Systems of complex difference equations of Malmquist type[J].Acta Mathematica Sinica, 2012, 55(20):293-300.
[14] GAO Lingyun. The growth order of solutions of systems of complex difference equations[J].Acta Mathematica Scientia, 2013, 33B(3):814-820.
[15] LI Huaxian, GAO lingyun. Meromorphic solutions of a type of systems of complex difference equations[J]. Journal of Mathematics, 2014, 34(4):662-670.
[16] 王钥,张庆彩.两类复差分方程组的亚纯允许解[J].应用数学学报,2015,38(1):80-88. WANG Yue, ZHANG Qingcai. Admissible meromorphic solutions of two types of systems of complex difference equations[J].Atca Mathematicae Applicatae Sinica, 2015, 38(1):80-88.
[17] GAO Lingyun. Estimates of N-function and m-function of meromorphic solutions of systems of difference equations[J].Acta Mathematica Scientia, 2012, 32B(4):1495-1502.
[18] 王钥,张庆彩,杨明华.复差分-微分方程组的解的增长级[J].数学物理学报,2014,34A(6):1337-1347. WANG Yue, ZHANG Qingcai, YANG Minghua. The growth of solutions of systems of complex difference-differential equations[J]. Acta Mathematica Scientia, 2014, 34A(6):1337-1347.
[19] WEISSENBORN G. On the theorem of Tumura and Clunie [J].The Bulletin of the London Mathematical Society, 1986, 18(4):371-373.
[20] LAINE I, RIEPPO J, SILNENNOINEN H. Remarks on complex difference equations[J].Computational Methods and function Theory, 2005, 5(1):77-88.
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