Abstract
In this paper, we mainly investigate properties of finite order transcendental meromorphic solutions of difference Painleve equations. If f is a finite order transcendental meromorphic solution of difference Painleve equations, then we get some estimates of the order and the exponent of convergence of poles of $\Delta f(z)$ , where $\Delta f(z)=f(z+1)-f(z)$ .
Highlights
Introduction and main resultsLet f be a function transcendental and meromorphic in the plane
We assume that the reader is familiar with the basic notions of Nevanlinna value distribution theory
Some results on the existence of meromorphic solutions for certain difference equations were obtained by Shimomura [ ] and Yanagihara [ ] years ago
Summary
Introduction and main resultsLet f be a function transcendental and meromorphic in the plane. Some results on the existence of meromorphic solutions for certain difference equations were obtained by Shimomura [ ] and Yanagihara [ ] years ago. Where ai and bi are polynomials, admits a non-rational meromorphic solution of finite order, max{p, q} ≤ .
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