ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG

doi:0.1016/S0252-9602(15)30087-4

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 195-202.doi: 0.1016/S0252-9602(15)30087-4

ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG

张月阳, 高宗升, 张继龙

LMIB & School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

收稿日期:2014-10-27 修回日期:2015-03-09 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Yueyang ZHANG,E-mail:zhangyy8911@gmail.com;Zongsheng GAO,E-mail:06712@buaa.edu.cn;Jilong ZHANG,E-mail:09017@buaa.edu.cn
基金资助:
The first author is supported by the NNSF of China(11171013, 11371225, 11201014), the YWF-14-SXXY-008 of Beihang University, and the Fundamental Research Funds for the Central University.

ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG

Yueyang ZHANG, Zongsheng GAO, Jilong ZHANG

LMIB & School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

Received:2014-10-27 Revised:2015-03-09 Online:2016-01-30 Published:2016-01-30
Supported by:
The first author is supported by the NNSF of China(11171013, 11371225, 11201014), the YWF-14-SXXY-008 of Beihang University, and the Fundamental Research Funds for the Central University.

摘要/Abstract

摘要：

In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equations f(z)ⁿ+P_n-1(f)=0, where n≥2 and P_n-1(f) is a difference polynomial of degree at most n-1 in f with small functions as coefficients.Moreover, we give two examples to show that one conjecture proposed by Yang and Laine [2] does not hold in general if the hyper-order of f(z) is no less than 1.

关键词: growth, meromorphic solutions, difference equations, conjectures

Abstract:

Key words: growth, meromorphic solutions, difference equations, conjectures

中图分类号:

30D35

张月阳, 高宗升, 张继龙. ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG[J]. 数学物理学报(英文版), 2016, 36(1): 195-202.

Yueyang ZHANG, Zongsheng GAO, Jilong ZHANG. ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG[J]. Acta mathematica scientia,Series B, 2016, 36(1): 195-202.

参考文献

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ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG

ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG

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