Value Distribution of Meromorphic Solutions of Certain Non-Linear Difference Equations
Acta Mathematica Scientia(2019)
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 Δ f ( z ) and divided difference Δ f(z)f(z) are estimated. Furthermore, we study the forms of rational solutions of the above equation.
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Key words
Non-linear difference equation, meromorphic solution, rational solution, value distribution, 30D35, 34M05, 39B32
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