Some Properties of Solutions for Some q-Difference Equations Containing Painlevé Equation

Abstract

The existence and growth of meromorphic solutions f(z) for some q-difference equations are studied, and some estimates for the exponent of convergence of poles of Δqf, Δq2f, Δqf/f, and Δq2f/f are also obtained. Our theorems are improvements and extensions of the previous results.