两类非线性差分方程有限级亚纯解的性质
Properties of Finite Order Meromorphic Solutions of Two Classes of Nonlinear Difference Equations

DOI: 10.12677/PM.2016.63029, PP. 190-194

Keywords: 差分方程，亚纯函数，Nevanlinna理论
Difference Equation, Meromorphic Function, Nevanlinna Theory

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Abstract:

本文主要研究两类非线性差分方程的有限级亚纯解，得到了一些关于解的性质，并给出了一些例子。
This paper is mainly to consider the finite order meromorphic solutions of two classes of nonlinear difference equations. Some results on the properties of the solutions are proved and examples are provided.

References

[1]	Hayman, W. (1964) Meromorphic Functions. Clarendon Press, Oxford.
[2]	Laine, I. (1993) Nevanlinna Theory and Complex Differential Equations. W. de Gruyter, Berlin. http://dx.doi.org/10.1515/9783110863147
[3]	杨乐. 值分布论及其新研究[M]. 北京: 科学出版社, 1982.
[4]	Rieppo, J. (2015) Malmquist-Type Results for Difference Equations with Periodic Coefficients. Computa-tional Methods and Function Theory, 15, 449-457. http://dx.doi.org/10.1007/s40315-015-0109-z
[5]	Ozawa, M. (1978) On the Existence of Prime Periodic Entire Functions. Kodai Mathematical Seminar Reports, 29, 308-321. http://dx.doi.org/10.2996/kmj/1138833654
[6]	Halburd, R.G. and Korhonen, R.J. (2007) Finite-Order Mero-morphic Solutions and the Discrete Painlevé Equations. Proceedings of the London Mathematical Society, 94, 443-474. http://dx.doi.org/10.1112/plms/pdl012
[7]	Chiang, Y.M. and Feng, S.J. (2009) On the Growth of Logarithmic Differences, Difference Quotients and Logarithmic Derivatives of Meromorphic Functions. Transactions of the American Mathematical Society, 7, 3767-3791. http://dx.doi.org/10.1090/S0002-9947-09-04663-7
[8]	Halburd, R.G. and Korhonen, R.J. (2006) Nevanlinna Theory for the Difference Operator. Annales Academi？ Scientiarum Fennic？ Mathematica, 31, 463-478.

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