一类费马型微分–差分方程解的问题
Solution on Differential-Difference Equation of Fermat-Type
DOI: 10.12677/PM.2020.103023, PDF,    国家自然科学基金支持
作者: 邓炳茂:广东金融学院金融数学与统计学院,广东 广州
关键词: 费马型方程整函数微分–差分方程Fermat-Type Equation Entire Function Differential-Difference Equation
摘要: 本文主要研究了以下费马型微分–差分方程的有穷级整函数解的情形,[f′(z)]2+[ Δckf(z)-f(z)]2=1并获得了一些有趣的结论。
Abstract: In this paper, we mainly discussed entire solutions with finite order of the following Fermat type differential-difference equation [f′(z)]2+[ Δckf(z)-f(z)]2=1 and obtained some interesting results.
文章引用:邓炳茂. 一类费马型微分–差分方程解的问题[J]. 理论数学, 2020, 10(3): 162-166. https://doi.org/10.12677/PM.2020.103023

参考文献

[1] Hayman, W.K. (1964) Meromorphic Functions. Clarendon Press, Oxford.
[2] Yang, L. (1993) Value Distribution Theory. Springer-Verlag, Berlin.
[3] Yi, H.X. and Yang, C.C. (2003) Uniqueness Theory of Meromorphic Functions. Science Press, Beijing.
[4] Gross, F. (1966) On the Equation fn + gn = 1. Bulletin of the American Mathematical Society, 72, 86-88. [Google Scholar] [CrossRef
[5] Gross, F. (1966) On the Equation fn + gn = hn. The American Mathematical Monthly, 73, 1093-1096. [Google Scholar] [CrossRef
[6] Yang, C.C. and Li, P. (2004) On the Transcendental Solutions of a Certain Type of Nonlinear Differential Equations. Archiv der Mathematik, 82, 442-448. [Google Scholar] [CrossRef
[7] Chen, M.F., Gao, Z.S. and Du, Y.F. (2017) Existence of Entire Solutions of Some Non-Linear Differential-Difference Equations. Journal of Inequalities and Applications, 90, 17 p. [Google Scholar] [CrossRef] [PubMed]
[8] 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
[9] Laine, I., Rieppo, J. and Silvennoinen, H. (2005) Remarks on Complex Difference Equations. Computational Methods and Function Theory, 5, 77-88. [Google Scholar] [CrossRef
[10] Halburd, R.G. and Korhonen, R.J. (2006) Difference Analogue of the Lemma on the Logarithmic Derivative with Applications to Difference Equations. Journal of Mathematical Analysis and Applications, 314, 477-487. [Google Scholar] [CrossRef
[11] Liu, K., Cao, T.B. and Cao, H.Z. (2012) Entire Solutions of Fermat Type Differential-Difference Equations. Archiv der Mathematik, 99, 147-155. [Google Scholar] [CrossRef
[12] Liu, K. (2015) Fermat Type Differential and Difference Equations. Electronic Journal of Differential Equations, 159, 1-10. [Google Scholar] [CrossRef
[13] Gao, L.Y. (2017) On Entire Solutions of Two Types of Systems of Complex Differential-Difference Equation. Acta Mathematica Scientia, 37B, 187-194. [Google Scholar] [CrossRef
[14] 高凌云. 关于一类复微分-差分方程组的解[J]. 数学年刊, 2017, 38A(1): 23-30.
[15] Gao, L.Y. (2016) Entire Solutions of Two Types of Systems of Complex Differential-Difference Equations. Acta Mathematica Scientia, 59, 677-684.