Value Distribution of Meromorphic Solutions of Certain Non-Linear Difference Equations

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.