与差分方程相关的唯一性问题
Uniqueness Problem of Merpmorphic Function Concerning Difference Equation
摘要:
本文主要研究了差分方程f (z+c)-f(z)=R(z)的一个有穷级亚纯函数解f(z)与g(z) CM分担0，1，∞的唯一性问题，补充并推广了崔宁，陈宗煊等人2017年的结论。
Abstract:
This paper studied the uniqueness of a finite order meromorphic solution f(z) of the difference equation f(z+c)-f(z)=R(z) sharing 0, 1, ∞ CM with meromorphic g(z). Our results sup-plemented and improved the result due to Cui and Chen in 2017.
参考文献
|
[1]
|
杨乐. 值分布及其新研究[M]. 北京: 科学出版社, 1982: 5-13.
|
|
[2]
|
Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromorphic Functions. Science Press, Beijing, 1-13.
|
|
[3]
|
Hayman, W.K. (1964) Mermorphic Functions. Clarendon Press, Oxford, 4-10.
|
|
[4]
|
Nevanlinna, R. (1929) Théorème de Picard-Borel et la théorie des fonctions méromorphes. Gauthier-Villars, Paris. [Google Scholar] [CrossRef]
|
|
[5]
|
Li, Y.H. and Qiao, J.Y. (2000) The Uniqueness of Meromorphic Functions Concerning Small Functions. Science in China, Series A, 43, 581-590. [Google Scholar] [CrossRef]
|
|
[6]
|
Li, P. and Yang, C.C. (2001) Uniqueness Theorems on Entire Functions and Their Derivatives. Journal of Mathematical Analysis and Applications, 253, 50-57. [Google Scholar] [CrossRef]
|
|
[7]
|
Chen, Z.X. and Yi, H.X. (2013) On Sharing Values of Meromorphic Functions and Their Differences. Results in Mathematics, 63, 557-565.
|
|
[8]
|
Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J. and Zhang, J.L. (2009) Value Sharing Results for Shifts of Meromorphic Functions, and Sufficient Conditions for Periodicity. Journal of Mathematical Analysis and Applications, 355, 352-363. [Google Scholar] [CrossRef]
|
|
[9]
|
崔宁, 陈宗煊. 一类线性差分方程的亚纯解与一个亚纯函数分担3个值的唯一性[J]. 数学年刊, 2017，38A(1): 13-22.
|
|
[10]
|
Chiang, Y.M. and Feng, S.J. (2008) On the Nevanlinna Characteristic of f(z+η) and Difference Equations in the Complex Plane. The Ramanujan Journal, 16, 105-129. [Google Scholar] [CrossRef]
|