We derive a special form of the $ q $ -difference equations whose solutions existin the form of a Dulac series.We find the coefficients of theDulac series from some algebraic difference equations having a polynomial solution under appropriate conditions.An example is given of a $ q $ -difference equation which demonstrates the lack of upper bounds for thedegrees of these polynomial solutions.We provide an upper bound for the degrees of the polynomialcoefficients in terms of the coefficient degrees of the initial segment of the Dulac series.We also give some examples of calculating the expansions of solutions to $ q $ -differenceequations in the form of Dulac series.
