Electron. J. Differential Equations, Vol. 2020 (2020), No. 14, pp. 1-14.

Existence of rational solutions for q-difference Painleve equations

Hong Yan Xu, Jin Tu

This article studies properties of meromorphic solutions for several types of q-difference Painleve equations. We obtain conditions for the existence, and the form of rational solutions for two classes of q-difference Painleve equations. Also for a solution f we obtain results about the fixed points, the exponents of convergence of poles of $f,\Delta_q f,(\Delta_qf)/f$. Our results extend previous theorems given in the references.

Submitted January 13, 2019. Published February 5, 2020.
Math Subject Classifications: 39A13, 30D35.
Key Words: Rational solution; q-difference Painleve equation; fixed point.

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Hong Yan Xu
School of Mathematics and Computer Science
Shangrao Normal University
Shangrao Jiangxi 334001, China
email: xhyhhh@126.com
Jin Tu
Department of Mathematics
Jiangxi Normal University
Nanchan, Jiangxi 330022, China
email: tujin2008@sina.com

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