Advances in Difference Equations
Volume 2005 (2005), Issue 2, Pages 173-192
Periodic solutions of nonlinear second-order difference equations
1Department of Mathematics, North Carolina State University, P.O. Box 8205, Raleigh 27695-8205, NC, USA
2Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill 27599, NC, USA
Received 6 August 2004
Copyright © 2005 Jesús Rodriguez and Debra Lynn Etheridge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form , where and is continuous. In our main result we assume that exhibits sublinear growth and that there is a constant such that whenever . For such an equation we prove that if is an odd integer larger than one, then there exists at least one -periodic solution unless all of the following conditions are simultaneously satisfied: , , and is an even multiple of .