On difference equations concerning Schwarzian equation

Consider the difference equation [Δ^3f(z)/Δ f(z)-3/2(Δ^2f(z)/Δ f(z))^2]^k =P(z,f(z))/Q(z,f(z)), where P(z,f) and Q(z,f) are prime polynomials in f(z) with _fP=p, _fQ=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 Δ f(z) and divided difference Δ f(z)/f(z) .