一类差分方程的亚纯解与亚纯函数分担3个值的唯一性

崔宁, 陈宗煊

崔宁, 陈宗煊. 一类差分方程的亚纯解与亚纯函数分担3个值的唯一性[J]. 华南师范大学学报(自然科学版), 2016, 48(4): 83-87. DOI: 10.6054/j.jscnun.2015.12.015
引用本文: 崔宁, 陈宗煊. 一类差分方程的亚纯解与亚纯函数分担3个值的唯一性[J]. 华南师范大学学报(自然科学版), 2016, 48(4): 83-87. DOI: 10.6054/j.jscnun.2015.12.015
CUI Ning, CHEN Zongxuan*. Unicity for Meromorphic Solutions of Some Difference Equations Sharing Three Values with Any Meromorphic Functions[J]. Journal of South China Normal University (Natural Science Edition), 2016, 48(4): 83-87. DOI: 10.6054/j.jscnun.2015.12.015
Citation: CUI Ning, CHEN Zongxuan*. Unicity for Meromorphic Solutions of Some Difference Equations Sharing Three Values with Any Meromorphic Functions[J]. Journal of South China Normal University (Natural Science Edition), 2016, 48(4): 83-87. DOI: 10.6054/j.jscnun.2015.12.015

一类差分方程的亚纯解与亚纯函数分担3个值的唯一性

基金项目: 

国家自然科学基金项目(11171119); 广东省自然科学基金项目(2014A030313422)

详细信息
    作者简介:

    陈宗煊, 教授, Email: chzx@vip.sina.com.

    通讯作者:

    陈宗煊, 教授, Email: chzx@vip.sina.com.

  • 中图分类号: O174.5

Unicity for Meromorphic Solutions of Some Difference Equations Sharing Three Values with Any Meromorphic Functions

  • 摘要: 利用亚纯函数的Nevanlinna值分布理论和分类讨论的思想方法, 研究了差分方程a1(z)f(z+1)+a0(z)f(z)=0的有穷级亚纯解f(z)与任一亚纯函数g(z)分担0, 1, CM时的唯一性问题, 得到f(z)g(z)或者f(z)g(z)1, 其中a1(z)和a0(z)是非零多项式且满足a1(z)+a0(z)0.
    Abstract: 〖JP3〗By utilizing Nevanlinna's value distribution theory of meromorphic functions and categorized discussion method, the uniqueness of a finite-order meromorphic solution f(z) of the difference equation a1(z)f(z+1)+a0(z)f(z)=0 〖JP+1〗sharing 0, 1, 〖KG-1mm〗CM with any meromorphic function g(z) is investigated, and the result is given that f(z)〖JP2〗g(z) or f(z)g(z)1 under the above condition, where a1(z) and a0(z) are nonzero polynomials satisfying a1(z)+a0(z)0.〖JP〗
  • 期刊类型引用(2)

    1. 吴丽镐,柴富杰,陈宝琴. 一阶线性差分方程解的唯一性. 南昌大学学报(理科版). 2023(05): 416-420+425 . 百度学术
    2. Hongjin LIN,Junfan CHEN,Shuqing LIN. Uniqueness of Meromorphic Solutions for a Class of Complex Linear Differential-Difference Equations. Journal of Mathematical Research with Applications. 2022(04): 331-348 . 必应学术

    其他类型引用(2)

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  • 被引次数: 4
出版历程
  • 收稿日期:  2015-11-10
  • 刊出日期:  2016-07-24

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