Acta mathematica scientia, Series B >
ON PROPERTIES OF q-DIFFERENCE EQUATIONS
Received date: 2010-03-29
Online published: 2012-03-20
Supported by
This project was supported by the National Natural Science Foundation of China (11171119, 11126145, 11026096) and the Nature Science Foundation of Jiangxi Province in China (20114BAB211003).
In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qi = qi.
ZHENG Xiu-Min , CHEN Zong-Xuan . ON PROPERTIES OF q-DIFFERENCE EQUATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 724 -734 . DOI: 10.1016/S0252-9602(12)60052-6
[1] Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964
[2] Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin: Walter de Gruyter, 1993
[3] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions. Dordrecht: Kluwer Academic Publishers Group, 2003
[4] Yang L. Value Distribution Theory. Berlin: Springer-Verlag, 1993
[5] Barnett D, et al. Nevanlinna Theory for the q-Difference Equations. Proc Roy Soc Edinburgh Sect A, 2007, 137: 457–474
[6] Bergweiler W, Langley J K. Zeros of Differences of Meromorphic Functions. Math Proc Cambridge Phil Soc, 2007, 142: 133–147
[7] Chen Z X, Shon K H. On Zeros and Fixed Points of Differences of Meromorphic Functions [J]. J Math Anal Appl, 2008, 344(1): 373–383
[8] Chen Z X, Huang Z B, Zheng X M. On Properties of Difference Polynomials. Acta Mathematica Scientia, 2011, 31B(2): 627–633
[9] Halburd R G, Korhonen R J. Nevanlinna Theory for the Difference Operator. Ann Acad Sci Fenn Math, 2006, 31: 463–478
[10] Laine I, Yang C C. Clunie Theorems for Difference and q-Difference Polynomials. J London Math Soc, 2007, 76: 556–566
[11] Ablowitz M J, Halburd R G, Herbst B. On the Extension of the Painlev´e Property to Difference Equations. Nonlinearity, 2000, 13: 889–905
[12] Bergweiler W, Ishizaki K, Yanagihara N. Meromorphic Solutions of Some Functonal Equations. Methods Appl Anal, 1998, 5(3): 248–258 (Correction: Methods Appl Anal, 1999, 6(4): 617–618)
[13] Chen Z X, Huang Z B, Zhang R R. On Difference Equations Concerning Gamma Functions. Acta Math Scientia, 2011, 31B(4): 1281–1294
[14] Gundersen G, et al. Meromorphic Solutions of Generalized Schr¨oder Equations. Aequationes Math, 2002, 63: 110–135
[15] Halburd R G, Korhonen R J. Existence of Finite-Order Meromorphic Solutions as a Detector of Integrability in Difference Equations. Phys D, 2006, 218: 191–203
[16] Heittokangas J, et al. Complex Difference Equations of Malmquist Type. Comput Methods Funct Theory, 2001, 1(1): 27–39
[17] Heittokangas J, et al. Meromorphic Solutions of Some Linear Functional Equations. Aequationes Math, 2000, 60: 148–166
[18] Ishizaki K. Hypertranscendency of Meromorphic Solutions of a Linear Functional Equation. Aequationes Math, 1998, 56: 271–283
[19] Laine I, Rieppo J, Silvennoinen H. Remarks on Complex Difference Equations. Comput Methods Funct Theory, 2005, 5(1): 77–88
[20] Zheng X M, Chen Z X. Growth of Meromorphic Solutions of Some Difference Equations. Appl Anal Discrete Math, 2010, 4(2): 309–321
[21] Zheng X M, Chen Z X. Some Properties of Meromorphic Solutions of q-Difference Equations. J Math Anal Appl, 2010, 361(2): 472–480
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