华东师范大学学报（自然科学版） >

2018 , Vol. 2018 >Issue 1: 50 - 58

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.01.006

数学

几类微分与差分方程组的亚纯解

  • 杨琰琰 ,
  • 魏文龙 ,
  • 黄志刚
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  • 苏州科技大学 数理学院, 江苏 苏州 215009
杨琰琰,女,硕士研究生,研究方向为复分析.E-mail:1139269431@qq.com.

收稿日期: 2017-02-27

  网络出版日期: 2018-01-11

基金资助

国家自然科学基金（11001057）；江苏省自然科学基金（BK2010234）；苏州科技大学科研基金（xkq201405）；苏州科技大学研究生科研创新项目（SKYCX16-001，SKYCX16-007）

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Meromorphic solutions of some type of system of differential and difference equations

  • YANG Yan-yan ,
  • WEI Wen-long ,
  • HUANG Zhi-gang
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  • College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215009, China

Received date: 2017-02-27

  Online published: 2018-01-11

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摘要

文章考察了差分方程组

亚纯解的性质，其中n ≥ 4，p1（z）、p2（z）是不为零的多项式，h1（z），h2（z）是整函数.应用值分布理论，得到了该方程组的解是唯一的.此外，文章还讨论了满足一些特殊类微分差分方程构成的方程组存在有限级亚纯解的条件.

关键词： Nevanlinna理论; 方程组; 微分差分方程; 亚纯解

本文引用格式

杨琰琰 , 魏文龙 , 黄志刚 . 几类微分与差分方程组的亚纯解[J]. 华东师范大学学报（自然科学版）, 2018 , 2018(1) : 50 -58 . DOI: 10.3969/j.issn.1000-5641.2018.01.006

Abstract

This article investigates some properties of meromorphic solutions of the type of system of differential-difference equations of the following form

where n ≥ 4,p1(z)、p2(z) are non-zero polynomials, and h1(z),h2(z) are entire functions. By using Nevanlinna theorem, we have obtained the solution of above equation is unique. We also discuss the conditions for several types of system of differential-difference equations if the systems of equations actually pose meromorphic solutions of finite order.

Key words： Nevanlinna theory; system of equations; differential-difference equation; meromorphic solution

参考文献

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[3] YANG C C. On entire solutions of a certain type of nonlinear differential equation[J]. Bull Austral Math Soc, 2001, 64(3):377-380.
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[6] LI H C, GAO L Y. Meromorphic solutions of a type of system of complex differential-difference equations[J]. Acta Mathematica Sinica, 2015, 35B(1):195-206.
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