Periodic Solutions of Periodic Difference Equations by Schauder’s Theorem

  • Tetsuo Furumochi Department of Mathematics, Shimane University, 1060 Nishikawatsucho, Matsue 690-8504, Japan.
Keywords: Periodic solutions, difference equations, fixed point theorem

Abstract

In this paper, we discuss the existence problem of periodic solutions of the periodic difference equation

x(n + 1) = f(n, x(n)),  nZ

and the periodic difference equation with infinite delay

x(n + 1) = f(n, xn),  nZ,

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.

Published
2009-08-01
How to Cite
[1]
T. Furumochi, “Periodic Solutions of Periodic Difference Equations by Schauder’s Theorem”, CUBO, vol. 11, no. 3, pp. 55–63, Aug. 2009.