一类微分方程组的亚纯解
Meromorphic Solutions to Some Systems of Difference-Differential Equations
DOI: 10.12677/PM.2020.109096, PDF,  被引量    科研立项经费支持
作者: 徐 慧, 张蒙蒙：中国石油大学(华东)理学院，山东 青岛
关键词: Nevanlinna理论；差分–微分方程；亚纯解；超越阶；小函数；
摘要: 本文主要研究某些给定的微分方程组的ρ2（f）<1的整体解或亚纯解的存在性，并获得一些有意义结果。并且，如果考虑的方程组允许超越解的存在，那么我们可以获得求解的精确表达。我们的结果改进和补充了前人的研究成果。
Abstract: In this paper, we will mainly study further on the existence of entire or meromorphic solutions with ρ2（f）<1 of some given systems of difference-differential equations, and obtain some interesting results. And if the considered systems admit a transcendental entire solution, then we can obtain the precise expression of the solution. Our results improve and complement the previous research results.
文章引用：徐慧, 张蒙蒙. 一类微分方程组的亚纯解[J]. 理论数学, 2020, 10(9): 837-842. https://doi.org/10.12677/PM.2020.109096

参考文献

[1] Hayman, W.K. (1964) Meromorphic Functions. Clarendon Press, Oxford.
[2] Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromorphic Functions. Science Press, Beijing/New York. [Google Scholar] [CrossRef] 
[3] Chen, Z.X. (2014) Complex Differences and Difference Equations. Science Press, Beijing. [Google Scholar] [CrossRef] 
[4] Liu, K. and Yang, L.Z. (2013) On Entire Solutions of Some Differen-tial-Difference Equations. Computational Methods and Function Theory, 13, 433-447. [Google Scholar] [CrossRef] 
[5] Yang, C.C. and Laine, I. (2010) On Analogies between Nonlinear Difference and Differential Equations. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 86, 10-14. [Google Scholar] [CrossRef] 
[6] Gross, F. (1966) On the Equation fn + gn = 1. Bulletin of the American Mathematical Society, 72, 86-88. [Google Scholar] [CrossRef] 
[7] Montel, P. (1927) Lecons sur les familles normales de fonctions analytiques et leurs applications. GauthierVillars, Paris, 135-136. (in French)
[8] Iyer, G. (1939) On Certain Functional Equations. The Journal of the Indian Mathematical Society, 3, 312-315.
[9] Yang, C.C. (1970) A Generalization of a Theorem of P. Montel on Entire Functions. Proceedings of the American Mathematical Society, 26, 332-334. [Google Scholar] [CrossRef] 
[10] Tang, J.F. and Liao, L.W. (2007) The Tran-scendental Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations. Journal of Mathematical Analysis and Applications, 334, 517-527. [Google Scholar] [CrossRef] 
[11] Yang, C.C. (1972) On Dificiencies of Differential Polynomials, II. Mathematische Zeitschrift, 125, 107-112. [Google Scholar] [CrossRef] 
[12] Halburd, R.G., Korhonen, R.J. and Tohge, K. (2014) Holomorphic Curves with Shift-Invariant Hyperplane Preimages. Transactions of the American Mathematical Society, 366, 4267-4298. [Google Scholar] [CrossRef] 
[13] Gao, L.Y. (2017) On Entire Solutions of Two Types of Systems of Complex Differential-Difference Equations. Acta Mathematica Scientia, 37B, 187-194. [Google Scholar] [CrossRef] 

为你推荐