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 Delta f(z) and divided difference Delta f(z)/f(z) are estimated. Furthermore, we f(z) study the forms of rational solutions of the above equation.