Taiwanese Journal of Mathematics

MEROMORPHIC SOLUTIONS OF DIFFERENCE EQUATION $f(z+1)=R\circ f(z)$

Zhang Jie

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Abstract

In this paper, we investigate the solutions of difference equation $f(z+1) = R \circ f(z)$ by utilizing Nevanlinna theory, where $R(z)$ is a rational function. And we also research the quantity of zeroes, poles, fixed points, and Borel exceptional values of the solutions.

Article information

Source
Taiwanese J. Math., Volume 18, Number 1 (2014), 27-37.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706329

Digital Object Identifier
doi:10.11650/tjm.18.2014.2747

Mathematical Reviews number (MathSciNet)
MR3162111

Zentralblatt MATH identifier
1357.30021

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 34M10: Oscillation, growth of solutions

Keywords
uniqueness difference equation order

Citation

Jie, Zhang. MEROMORPHIC SOLUTIONS OF DIFFERENCE EQUATION $f(z+1)=R\circ f(z)$. Taiwanese J. Math. 18 (2014), no. 1, 27--37. doi:10.11650/tjm.18.2014.2747. https://projecteuclid.org/euclid.twjm/1499706329


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References

  • W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
  • I. Laine, Nevanlinna Theory and Complex Differential Equations, Studies in Math, de Gruyter, Berlin, 1993, p. 15.
  • C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, Second Printed in 2006.
  • L. Yang, Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993.
  • Niro Yanagihara, Meromorphic solutions of some difference equations, Funkcialaj. Ekvacioj., 23 (1980), 309-326.
  • J. H. Zheng, A note on the Riccati equation, J. Math. Anal. Appl, 190 (1995), 285-193.
  • Z. X. Chen, On the hyper-order of solutions of some second order linear differential equations, Acta Mathematica Sinica, English series, 18(1) (2002), 79-88.
  • Z. X. Chen and K. H. Shon, Some Results on Difference Riccati Equations, Acta Mathematica Sinica, English series, 27(6) (2011), 1091-1100.
  • J. Heittokangas, R. Korhonen and I. Laine, Complex difference eqaution of Malmquist type, Comput. Methods Funct. Theory, 1 (2001), 27-39.
  • I. Laine and C. C. Yang, Clunie theorem for difference and $q$-difference polynomials, J. London Math. Soc., 76(3) (2007), 556-566.
  • Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of $f(z+\eta)$ and difference equations in the complex plane, Ramanujian J., 16 (2008), 105-129.