The zeros of difference of meromorphic solutions for the difference Riccati equation

Abstract

In this paper, we mainly investigate some properties of the transcendental meromorphic solution f (z) for the difference Riccati equation f (z + 1) = p(z)f (z)+q(z) f (z)+s(z) . We obtain some estimates of the exponents of the convergence of the zeros and poles of f (z) and the difference f (z) = f (z + 1) -f (z). MSC: 30D35; 39B12