VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS  

作　　者：Minfeng CHEN Zongsheng GAO Jilong ZHANG 陈敏风;高宗升;张继龙(School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China;LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China)

机构地区：[1]School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China [2]LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

出　　处：《Acta Mathematica Scientia》2019年第4期1173-1184,共12页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11371225);National Natural Science Foundation of Guangdong Province(2016A030313686)

摘　　要：In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference ?f(z) and divided difference?f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

关 键 词：NON-LINEAR DIFFERENCE equation MEROMORPHIC SOLUTION RATIONAL SOLUTION value dist ribution 

分 类 号：O[理学]