Value distribution of meromorphic solutions of certain difference Painlevé equations. (English) Zbl 1183.30026

Summary: The Borel exceptional value and the exponents of convergence of poles, zeros, and fixed points of finite order transcendental meromorphic solutions for difference Painlevé \(I\) and \(II\) equations are estimated. The forms of rational solutions of the difference Painlevé \(II\) equation and the autonomous difference Painlevé \(I\) equation are also given. It is also proved that the non-autonomous difference Painlevé \(I\) equation has no rational solution.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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