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Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations

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  • Shuang-Ting Lan
  • Zong-Xuan Chen

Abstract

In this paper, we mainly study the properties of transcendental meromorphic solutions f(z) of difference Painlevé equations w(z + 1)w(z − 1)(w(z) − 1) = η(z)w2 (z) − λ(z)w(z) and w(z + 1)w(z − 1)(w(z)−1) = η(z)w(z) and obtain precise estimations of the exponents of convergence of zeros, poles of Δf(z) and Δf(z)/f(z), and of fixed points of f(z + c) for any c ∈ ℂ.

Suggested Citation

  • Shuang-Ting Lan & Zong-Xuan Chen, 2014. "Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:782024
    DOI: 10.1155/2014/782024
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    1. Shuang-Ting Lan & Zong-Xuan Chen, 2014. "On Properties of Meromorphic Solutions of Certain Difference Painlevé III Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Shuang-Ting Lan & Zong-Xuan Chen, 2014. "On Properties of Meromorphic Solutions of Certain Difference Painlevé III Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, February.
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