Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions

Abstract

For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an}, {bn} 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.