复微分-差分方程组的整函数解

曾翠萍, 邓炳茂, 方明亮

数学学报 ›› 2019, Vol. 62 ›› Issue (1) : 123-136.

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PDF(433 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (1) : 123-136. DOI: 10.12386/A2019sxxb0010
论文

复微分-差分方程组的整函数解

    曾翠萍1, 邓炳茂2, 方明亮2
作者信息 +

Entire Solutions of Systems of Complex Differential-difference Equations

    Cui Ping ZENG1, Bing Mao DENG2, Ming Liang FANG2
Author information +
文章历史 +

摘要

利用值分布理论,研究了一类1阶复微分-差分方程
ω(n)(z)2 +[αω(z + c) - βω(z)]2=1
和复微分-差分方程组

是否存在有限级整函数解的问题.本文推广并改进了高凌云和刘凯等人的结果.

Abstract

In this paper, using theory of value distribution, we investigate whether a class of order n complex differential-difference equation
ω(n)(z)2 +[αω(z + c) - βω(z)]2=1
and a class of systems of order n complex differential-difference equations 

have entire solutions with finite order or not. Our results extend and improve the results due to Gao Lingyun and Liu Kai et al.

关键词

复微分-差分方程 / 超越整函数 / 亚纯函数

Key words

complex differential-difference equations / transcendental entire functions / meromorphic functions

引用本文

导出引用
曾翠萍, 邓炳茂, 方明亮. 复微分-差分方程组的整函数解. 数学学报, 2019, 62(1): 123-136 https://doi.org/10.12386/A2019sxxb0010
Cui Ping ZENG, Bing Mao DENG, Ming Liang FANG. Entire Solutions of Systems of Complex Differential-difference Equations. Acta Mathematica Sinica, Chinese Series, 2019, 62(1): 123-136 https://doi.org/10.12386/A2019sxxb0010

参考文献

[1] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z +η) and difference equations in the complex plane, Ramanujan J., 2008, 16(1):105-129.
[2] Gao L. Y., Entire solutions of two types of systems of complex differential-difference equations, Acta Math. Sin., Chin. Ser., 2016, 59(5):577-684.
[3] Gross F., On the equation fn + gn=1, Bull. Amer. Math. Soc., 1966, 72:86-88.
[4] Halburd R. G., Korhonen R. J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 2006, 314:477-487.
[5] Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[6] Laine I., Rieppo J., Silvennoinen H., Remarks on complex difference equations, Comput. Methods Funct. Theory, 2005, 5(1):77-88.
[7] Liu K., Cao T. B., Cao H. Z., Entire solutions of Fermat type differential-difference equations, Arch. Math., 2012, 99(5):147-155.
[8] Liu K., Yang L. Z., On entire solutions of some differential-difference equations, Comput. Methods Funct. Theory, 2013, 13(3):433-447.
[9] Yang C. C., Li P., On the transcendental solutions of a certain of nonlinear differential equations, Arch. Math., 2004, 82:442-448.
[10] Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[11] Yi H. X., Yang C. C., Theory of the Uniqueness of Meromorphic Function (in Chinese), Science Press, Beijing, 1995.

基金

国家自然科学基金资助项目(11371149);广东省教育厅科研项目(2017KTECX130);广东金融学院科研资助项目(20170502152,15XJ01-03)

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