The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations

摘要

The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations xn+1=F(n,xn,xn−1,…,xn−k), where k is a nonnegative integer, are studied. A method of analysis of bifurcation of periodic solutions in the nonautonomous difference equations are presented. We apply this result on the rational difference equation xn+1=(an+bnxn)/(xn−1).