Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 14, pp. 1-14.

Title: Existence of rational solutions for q-difference Painleve equations

Authors: Hong Yan Xu (Shangrao Normal Univ. Shangrao Jiangxi, China)
         Jin Tu (Jiangxi Normal Univ., Nanchan, Jiangxi, China)

Abstract:
 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 05, 2020.
Math Subject Classifications: 39A13, 30D35.
Key Words: Rational solution; q-difference Painleve equation; fixed point.