摘要：Consider the difference equation [ Δ 3 f ( z ) Δ f ( z ) − 3 2 ( Δ 2 f ( z ) Δ f ( z ) ) 2 ] k = P ( z , f ( z ) ) Q ( z , f ( z ) ) , $$\biggl[\frac{\Delta^"f(z)}{\Delta f(z)}-\frac", \biggl(\frac {\Delta^,f(z)}{\Delta f(z)} \biggr)^, \biggr]^{k} =\frac{P(z,f(z))}{Q(z,f(z))}, $$ where P ( z , f ) $P(z,f)$ and Q ( z , f ) $Q(z,f)$ are prime polynomials in f ( z ) $f(z)$ with deg f P = p , deg f Q = q $\deg_{f}P=p, \deg_{f}Q=q$ , and d = max { p , q } > 0 $d=\max\{p,q\}>0$ . We give the supremum of d, an estimation of the sum of Nevanlinna exceptional values of meromorphic solution f ( z ) $f(z)$ of the equation, and study the value distributions of their difference Δ f ( z ) $\Delta f(z)$ and divided difference Δ f ( z ) f ( z ) $\frac{\Delta f(z)}{f(z)}$ .
关键词：meromorphic solution ; difference ; Nevanlinna exceptional value
