On difference equations concerning Schwarzian equation

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