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

doi:10.1007/s10473-019-0419-8

Abstract

Abstract: 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.

Key words: Non-linear difference equation, meromorphic solution, rational solution, value distribution

CLC Number:

30D35

Minfeng CHEN, Zongsheng GAO, Jilong ZHANG. VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS[J].Acta mathematica scientia,Series B, 2019, 39(4): 1173-1184.

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