Eventually periodic solutions for difference equations with periodic coefficients and nonlinear control functions (Q1009430)

Summary: For nonlinear difference equations of the form \(x_{n}=F(n,x_{n - 1},\dots ,x_{n - m})\), it is usually difficult to find periodic solutions. We consider a class of difference equations of the form \(x_{n}=a_{n}x_{n - 1}+b_{n}f(x_{n - k})\), where \({a_{n}},\thinspace \thinspace {b_{n}}\) are periodic sequences and \(f\) is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results.