Open Access

Periodic solutions of nonlinear second-order difference equations

Advances in Difference Equations20052005:718682

https://doi.org/10.1155/ADE.2005.173

Received: 6 August 2004

Published: 31 May 2005

Abstract

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by (t + 1) + cy(t) = f (y(t)), where f: and β > 0 is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant uf (u) > 0 such that |u| ≥ β whenever c = 1. For such an equation we prove that if N is an odd integer larger than one, then there exists at least one N-periodic solution unless all of the following conditions are simultaneously satisfied: |b| < 2, N across-1(-b/2), and π is an even multiple of c ≠ 0.

Authors’ Affiliations

(1)
Department of Mathematics, North Carolina State University
(2)
Department of Mathematics, University of North Carolina at Chapel Hill

Copyright

© Rodriguez and Etheridge 2005