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Acta Mathematica Scientia

, Volume 39, Issue 1, pp 139–147 | Cite as

On Existence of Solutions of Difference Riccati Equation

  • Zongxuan Chen (陈宗煊)Email author
  • Kwang Ho Shon
Article
  • 1 Downloads

Abstract

Consider the difference Riccati equation xxxx, where A, B, C, D are meromorphic functions, we give its solution family with one-parameter \(H\left( {f\left( z \right)} \right) = \left\{ {{f_0}\left( z \right),f\left( z \right) = \frac{{\left( {{f_1}\left( z \right) - {f_0}\left( z \right)} \right)\left( {{f_2}\left( z \right) - {f_0}\left( z \right)} \right)}}{{Q\left( z \right)\left( {{f_2}\left( z \right) - {f_1}\left( z \right)} \right) + \left( {{f_2}\left( z \right) - {f_0}\left( z \right)} \right)}} + {f_0}\left( z \right)} \right\}\) , where Q(z) is any constant in C or any periodic meromorphic function with period 1, and f0(z), f1(z), f2(z) are its three distinct meromorphic solutions.

Key words

difference Riccati equation solution family order of growth 

2010 MR Subject Classification

30D35 39A10 

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Copyright information

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

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina
  2. 2.Department of Mathematics, College of Natural SciencesPusan National UniversityBusanKorea

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