scholarly journals Borel exceptional values of meromorphic solutions of Painlevé III difference equations

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Jilong Zhang ◽  
Hongxun Yi
Keyword(s):  
Difference Equations ◽  
Meromorphic Solutions ◽  
Borel Exceptional Values

scholarly journals Meromorphic Solutions of Linear Difference Equations with Polynomial Coefficients

2017 ◽  
Vol 59 (1) ◽  
pp. 159-168
Author(s):  
Y. Zhang ◽  
Z. Gao ◽  
H. Zhang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Necessary Conditions ◽  
Meromorphic Solution ◽  
Linear Difference Equation ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Polynomial Coefficients ◽  
Difference Analogue ◽  
Borel Exceptional Values

AbstractWe study the growth of the transcendental meromorphic solution f(z) of the linear difference equation:where q(z), p0(z), ..., pn-(z) (n ≥ 1) are polynomials such that p0(z)pn(z) ≢ 0, and obtain some necessary conditions guaranteeing that the order of f(z) satisfies σ(f) ≥ 1 using a difference analogue of the Wiman-Valiron theory. Moreover, we give the form of f(z) with two Borel exceptional values when two of p0(z), ..., pn(z) have the maximal degrees.

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 MEROMORPHIC SOLUTIONS OF q-DIFFERENCE EQUATIONS

2003 ◽  
Vol 57 (2) ◽  
pp. 265-276
Author(s):  
Ilham ELI ◽  
Niro YANAGIHARA
Keyword(s):  
Difference Equations ◽  
Meromorphic Solutions

Meromorphic Solutions of Complex Differential–Difference Equations

2017 ◽  
Vol 72 (4) ◽  
pp. 1759-1771 ◽  
Author(s):  
Kai Liu ◽  
Chang Jiang Song
Keyword(s):  
Difference Equations ◽  
Meromorphic Solutions
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