Periodic solutions of difference equations Original Research Article

In this paper, we discuss the existence of periodic solutions of periodic difference equations including View the MathML sourcex(n+1)=f(n,x(n)),n∈Z, Turn MathJax on where xx and ff are dd-vectors, and View the MathML sourceZ denotes the set of integers, as well as scalar autonomous difference equations including View the MathML sourcex(n)=−f(x(n−1)),n∈Z. Turn MathJax on First we state some recent results concerning periodic solutions of periodic difference equations. Then, we show the existence of periodic solutions of scalar autonomous difference equations by using Schauder’s fixed point theorem. We illustrate the results with some examples.