Periodic Solutions of Periodic Difference Equations by Schauder‘s Theorem

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Abstract

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.

Keywords

Periodic solutions , difference equations , fixed point theorem
  • Tetsuo Furumochi Department of Mathematics, Shimane University, 1060 Nishikawatsucho, Matsue 690-8504, Japan.
  • Pages: 55–63
  • Date Published: 2009-08-01
  • Vol. 11 No. 3 (2009): CUBO, A Mathematical Journal

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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.

Issue

Vol. 11 No. 3 (2009): CUBO, A Mathematical Journal

Section

Articles