scholarly journals The properties of solutions for several types of Painlevé equations concerning fixed-points, zeros and poles

2019 ◽  
Vol 17 (1) ◽  
pp. 1014-1024
Author(s):  
Hong Yan Xu ◽  
Xiu Min Zheng
Keyword(s):  
Fixed Points ◽  
Difference Equations ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations ◽  
Zeros And Poles

Abstract The purpose of this manuscript is to study some properties on meromorphic solutions for several types of q-difference equations. Some exponents of convergence of zeros, poles and fixed points related to meromorphic solutions for some q-difference equations are obtained. Our theorems are some extension and improvements to those results given by Qi, Peng, Chen, and Zhang.

scholarly journals Zeros, Poles, and Fixed Points of Meromorphic Solutions of Difference Painlevé Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang-Ting Lan ◽  
Zong-Xuan Chen
Keyword(s):  
Fixed Points ◽  
Painlevé Equations ◽  
Meromorphic Solutions ◽  
Painleve Equations

In this paper, we mainly study the properties of transcendental meromorphic solutionsf(z)of difference Painlevé equationsw(z+1)w(z-1)(w(z)-1)=η(z)w2(z)-λ(z)w(z)andw(z+1)w(z-1)(w(z)-1)=η(z)w(z)and obtain precise estimations of the exponents of convergence of zeros, poles ofΔf(z)andΔf(z)/f(z), and of fixed points off(z+c)for anyc∈ℂ.

scholarly journals Growth of Meromorphic Solutions of Some -Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Guowei Zhang
Keyword(s):  
Difference Equation ◽  
Fixed Points ◽  
Difference Equations ◽  
Meromorphic Solutions ◽  
Order Difference ◽  
Complex Difference ◽  
Complex Difference Equations ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
The Difference

We estimate the growth of the meromorphic solutions of some complex -difference equations and investigate the convergence exponents of fixed points and zeros of the transcendental solutions of the second order -difference equation. We also obtain a theorem about the -difference equation mixing with difference.

Sign in / Sign up

Export Citation Format

Share Document