ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

doi:10.1016/S0252-9602(13)60070-3

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1141-1152.doi: 10.1016/S0252-9602(13)60070-3

ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

黄志波|陈宗煊|李倩

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China； Department of Applied Mathematics, South China Agricultural University, Guangzhou 510640, China

收稿日期:2012-03-25 出版日期:2013-07-20 发布日期:2013-07-20
基金资助:
This project was supported by the National Natural Science Foundation of China (11171119)

ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

HUANG Zhi-Bo, CHEN Zong-Xuan, LI Qian

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China； Department of Applied Mathematics, South China Agricultural University, Guangzhou 510640, China

Received:2012-03-25 Online:2013-07-20 Published:2013-07-20
Supported by:
This project was supported by the National Natural Science Foundation of China (11171119)

摘要/Abstract

摘要：

In this paper, we present the properties on zeros, fixed points, poles, Borel exceptional value of finite order transcendental meromorphic solutions of complex difference
equation of Malmquist type
∑ⁿ_j₌₁f (z + c_j ) = R(f (z)) =P(f (z))Q(f (z))=a_pf(z)^p + a_p−1f (z)^p−1 + … + a₁f (z) + a₀/b_qf (z)^q+ b_q₋₁f (z)^q−1 + … + b₁f(z) + b₀,
where n(∈ N) ≥ 2, P(f(z)) and Q(f(z)) are relatively prime polynomials in f(z) with rational coefficients as (s = 0, 1, … , p) and bt (t = 0, 1, … , q) such that a0apbq 6≡ 0, and also consider the existence and the forms on rational solutions of this type of difference equations. Some examples are also listed to show that the assumptions of theorems, in certain senses, are the best possible.

关键词: zeros, poles, fixed-points, Borel exceptional value, difference equation

Abstract:

Key words: zeros, poles, fixed-points, Borel exceptional value, difference equation

中图分类号:

30D35

黄志波, 陈宗煊, 李倩. ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE[J]. 数学物理学报(英文版), 2013, 33(4): 1141-1152.

HUANG Zhi-Bo, CHEN Zong-Xuan, LI Qian. ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE[J]. Acta mathematica scientia,Series B, 2013, 33(4): 1141-1152.

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ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

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