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Results on solutions for several \(q\)-Painlevé difference equations concerning rational solutions, zeros, and poles. (English) Zbl 07290887
Summary: In this article, we discuss the problem about the properties on solutions for several types of \(q\)-difference equations and obtain some results on the exceptional values of transcendental meromorphic solutions \(f(z)\) with zero order, their \(q\)-differences \(\Delta_q f(z)=f(q z)-f(z)\), and divided differences \(\Delta_q f(z)/f(z)\). In addition, we also investigated the condition on the existence of rational solution for a class of \(q\)-difference equations. Our theorems are some extensions and supplement to those results given by Y. Liu and Y. Zhang [Adv. Difference Equ. 2018, Paper No. 282, 9 p. (2018; Zbl 1446.39019)] and X. Qi and L. Yang [Electron. J. Differ. Equ. 2015, Paper No. 59, 9 p. (2015; Zbl 1314.39002)].
MSC:
30-XX Functions of a complex variable
39-XX Difference and functional equations
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