摘要：In this paper, by using Nevanlinna value distribution theory, we consider a certain type of difference equation, which originates with the difference Painlevé I equation, f ( z + 1 ) + f ( z − 1 ) = A ( z ) f ( z ) + C ( z ) $f(z+1)+f(z-1)= rac{A(z)}{f(z)}+C(z)$ , where A ( z ) $A(z)$ , C ( z ) $C(z)$ are small meromorphic functions relative to f ( z ) $f(z)$ , and we obtain the existence and the forms of rational solutions. We also discuss the properties of the Borel exceptional value, zeros, poles, and fixed points of finite order transcendental meromorphic solutions.
