Brück猜想的一类微分和差分方程

张杰

数学学报 ›› 2013, Vol. 56 ›› Issue (1) : 61-66.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2013, Vol. 56 ›› Issue (1) : 61-66. DOI: 10.12386/A2013sxxb0007
论文

Brück猜想的一类微分和差分方程

    张杰
作者信息 +

One Certain Type of Differential and Difference Equations Related to Brück Conjecture

    Jie ZHANG
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文章历史 +

摘要

运用值分布以及Wiman-Valiron 理论研究了整函数与它的k阶导数分担某些小函数问题, 得到了一些涉及到Brück猜想的唯一性结果.

Abstract

We investigate the question that an entire function and its k-th derivative share some functions by utilizing Nevanlinna theory and Wiman-Valiron theory. We obtain some uniqueness theorems which are closely related to the Brück's conjecture in this direction.

关键词

唯一性 / 差分方程 / 增长级

Key words

uniqueness / difference equation / order

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张杰. Brück猜想的一类微分和差分方程. 数学学报, 2013, 56(1): 61-66 https://doi.org/10.12386/A2013sxxb0007
Jie ZHANG. One Certain Type of Differential and Difference Equations Related to Brück Conjecture. Acta Mathematica Sinica, Chinese Series, 2013, 56(1): 61-66 https://doi.org/10.12386/A2013sxxb0007

参考文献

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[4] Rubel L., Yang C. C., Values Shared by an Entire Function and Its Derivative, in: Complex Analysis, Kentucky, 1976. Pro. Conf. in: Lecture Notes in Math. Vol. 599, Springer-Verlag, Berlin, 1977: 101–103.

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[6] Gundersen G., Yang L. Z., Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl., 1998, 223: 88–95.

[7] Yang L. Z., Solution of a differential equation and its applications, Kodai. Math. J., 1999, 22: 458–464.

[8] Chang J. M., Zhu Y. Z., Entire functions that share a small function with their derivatives, J. Math. Appl., 2009, 351: 491–495.

[9] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z + η) and difference equations in the complex plane, Ramanujian J., 2008, 16: 105–129.

[10] Li X. M., Yi H. X., An entire function and its derivatives sharing a polynomial, J. Math. Anal. Appl., 2007, 330: 66–79.

基金

中央高校基本科研业务费专项资金资助项目(2011QNA25)

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