Abstract and Applied Analysis
Volume 2011 (2011), Article ID 635926, 12 pages
http://dx.doi.org/10.1155/2011/635926
Research Article

Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications

Rong Cheng

College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 28 November 2010; Revised 31 January 2011; Accepted 2 March 2011

Academic Editor: Elena Braverman

Copyright © 2011 Rong Cheng. 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.

Abstract

We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established.