Finite order solutions of difference equations, and difference Painlevé equations IV
Finite order solutions of difference equations, and difference Painlevé equations IV
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DOI：
10.1090/proc/13210
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发表时间：
2016-06
影响因子：
1.3
通讯作者：
Z. Wen
中科院分区：
文献类型：
--
作者：
Z. Wen
本文从非线性差分方程（w + w）（w + w）= P（z，w）Q（z，w）出发，其中P（z，w）和Q（r，w）是关于w（z）的多项式，没有与w（z）有关的小函数系数的公因子，给出了差分Painlevé方程IV（w + w）（w + w）=（w2 − a2）（w2 − b2）（w +（αz + β））2 + π的形式，其中a，B，α，β和π是与w有关的周期小函数.证明了如果上述差分方程至少存在一个有限级亚纯解w（z），则该差分方程可通过在w中的Möbius变换变换为差分Painlevé IV，除非w是差分Riccati方程的解.
In this paper, from the non-linear difference equation (w + w)(w + w) = P (z,w) Q(z,w) where P (z,w) and Q(r, w) are polynomials in w(z) without common factors having small function coefficients related to w(z), we present the form of difference Painlevé equation IV (w + w)(w + w) = (w2 − a2)(w2 − b2) (w + (αz + β))2 + π , where a, b, α, β and π are period small functions related to w. It shows that if the above difference equation admits at least one meromorphic solution w(z) of finite order, then the difference equation can be transformed by Möbius tranformation in w to difference Painlevé IV, unless w is the solution of difference Riccati equations.