Boundedness character of the recursive sequence xn=α+∏j=1kxn−jaj

The boundedness character of positive solutions of the difference equation in the title, where α>0α>0 and aj∈Raj∈R, j=1,k¯, ak≠0ak≠0, is studied here in terms of the roots of the following associated polynomial Pk(t)=tk−a1tk−1−a2tk−2−⋯−akPk(t)=tk−a1tk−1−a2tk−2−⋯−ak.