Value distribution of meromorphic solutions of certain difference Painlevé III equations.

In this paper, we investigate the difference Painlevé III equations w(z+1)w(z−1)(w(z)−1)2=w2(z)−λw(z)+μ<inline-graphic></inline-graphic> (λμ≠0<inline-graphic></inline-graphic>) and w(z+1)w(z−1)(w(z)−1)2=w2(z)<inline-graphic></inline-graphic>, and obtain some results about the properties of the finite order transcendental meromorphic solutions. In particular, we get the precise estimations of exponents of convergence of poles of difference Δw(z)=w(z+1)−w(z)<inline-graphic></inline-graphic> and divided difference Δw(z)w(z)<inline-graphic></inline-graphic>, and of fixed points of w(z+η)<inline-graphic></inline-graphic> (η∈C∖{0}<inline-graphic></inline-graphic>). [ABSTRACT FROM AUTHOR]