Periodic Solutions of Periodic Difference Equations by Schauder’s Theorem
In this paper, we discuss the existence problem of periodic solutions of the periodic difference equation
x(n + 1) = f(n, x(n)), n ∈ Z
and the periodic difference equation with infinite delay
x(n + 1) = f(n, xn), n ∈ Z,
where x and f are d-vectors, and Z denotes the set of integers. We show the existence of periodic solutions by using Schauder’s fixed point theorem, and illustrate an example.