Some difference results on Hayman conjecture and uniqueness

In this paper‎, ‎we show that for any finite order entire function‎ ‎$f(z)$‎, ‎the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no‎ ‎nonzero finite Picard exceptional value for all nonnegative integers‎ ‎$n‎, ‎s$ satisfying $n\geq 3$‎, ‎which can be viewed as a difference‎ ‎result on Hayman conjecture‎. ‎We also obtain some‎ ‎uniqueness theorems for difference polynomials of entire functions‎ ‎sharing one common value‎.