The Research For The Solutions Of Several Types Of Linear Difference Equations With Constant Coefficients

In this paper, we first discuss the structure for the solutions of the k-order linear difference equation with constant coefficients. By the introduction of the shift operator, we transfer the difference equation to an operator equation. The simple representation of general solutions of the difference equation is obtained by the operator method and some lemmas. Then, we discuss several types of k-order non-homogeneous linear difference equations with constant coefficients. According to the character of the equations, we transfer them to higher order homogeneous linear difference equations. By the representation of general solutions of the higher order homogeneous linear difference equations, we obtain a special solution of the original non-homogeneous linear difference equation, and then the general solutions of the non-homogeneous linear difference equation are obtained. The results in [9],[10] and [21] are generalized to the cases of k-order.