Meromorphic Solutions of Algebraic Difference Equations

It is shown that the difference equation where A(z) and B(z) are meromorphic functions, possesses a continuous limit to the differential equation which extends to solutions in certain cases. In addition, if (1) possesses two distinct transcendental meromorphic solutions, it is shown that these solutions satisfy an algebraic relation, and that their growth behaviors are almost the same in the sense of Nevanlinna under some conditions. Examples are given to discuss the sharpness of the results obtained. These properties are counterparts of the corresponding results on the algebraic differential equation (2).