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Some Results on the Painlevé III Difference Equations with Constant Coefficients
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) ( IF 0.3 ) Pub Date : 2020-09-01 , DOI: 10.3103/s1068362320020065
Lei Liu , Jilong Zhang

Abstract

In this paper, we investigate the following two Painlevé III equations: \(\overline{w}\underline{w}(w^{2}-1)=w^{2}+\mu\) and \(\overline{w}\underline{w}(w^{2}-1)=w^{2}-\lambda w\), where \(\overline{w}:=w(z+1)\), \(\underline{w}:=w(z-1)\) and \(\mu\) (\(\mu\neq-1\)) and \(\lambda\notin\{\pm 1\}\) are constants. We discuss the questions of existence of rational solutions, of Borel exceptional values and the exponents of convergence of zeros, poles and fixed points of transcendental meromorphic solutions of these equations.



中文翻译:

关于PainlevéIII常数差分方程的一些结果。

摘要

在本文中,我们研究了以下两个PainlevéIII方程:\(\ overline {w} \ underline {w}(w ^ {2} -1)= w ^ {2} + \ mu \)\(\ overline {w} \下划线{w}(w ^ {2} -1)= w ^ {2}-\ lambda w \),其中\(\ overline {w}:= w(z + 1)\)\ (\下划线{w}:= w(z-1)\)\(\ mu \)\(\ mu \ neq-1 \))和\(\ lambda \ notin \ {\ pm 1 \} \ )是常量。我们讨论了这些方程的先验亚纯解的有理解,Borel极值和零,极点和不动点的收敛指数的问题。

更新日期:2020-09-01
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