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Acta Mathematica Scientia

, Volume 39, Issue 4, pp 1173–1184 | Cite as

Value Distribution of Meromorphic Solutions of Certain Non-Linear Difference Equations

  • Minfeng Chen (陈敏风)Email author
  • Zongsheng Gao (高宗升)
  • Jilong Zhang (张继龙)
Article
  • 22 Downloads

Abstract

In this article, we consider the non-linear difference equation
$$(f(z + 1)f(z) - 1)(f(z)f(z - 1) - 1) = {{P(z,f(z))} \over {Q(z,f(z))}},$$
where P(z, f (z)) and Q(z,f (z)) are relatively prime polynomials in f (z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f (z), and the exponents of convergence of poles of difference Δf (z) and divided difference \({{{\rm{\Delta }}\;f(z)} \over {f(z)}}\) are estimated. Furthermore, we study the forms of rational solutions of the above equation.

Key words

Non-linear difference equation meromorphic solution rational solution value distribution 

2010 MR Subject Classification

30D35 34M05 39B32 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Minfeng Chen (陈敏风)
    • 1
    • 2
    Email author
  • Zongsheng Gao (高宗升)
    • 2
  • Jilong Zhang (张继龙)
    • 2
  1. 1.School of Mathematics and StatisticsGuangdong University of Foreign StudiesGuangzhouChina
  2. 2.LMIB and School of Mathematics and Systems ScienceBeihang UniversityBeijingChina

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