| 一类差分方程的亚纯解与亚纯函数分担3个值的唯一性 |
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| 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. |
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| 作者姓名： | 崔宁 陈宗煊 |
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| 作者单位： | 1.(华南师范大学数学科学学院,广州 510631) |
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| 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) |
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| 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.
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| 关 键 词： | 亚纯函数 差分方程 分担值 唯一性 |
| 收稿时间： | 2015-11-11 |
Unicity for Meromorphic Solutions of Some Difference Equations Sharing Three Values with Any Meromorphic Functions |
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| 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. |
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| Authors: | CUI Ning;CHEN Zongxuan |
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| Affiliation: | 1.(School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China) |
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| 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〗 |
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