Abstract and Applied Analysis
Volume 2012 (2012), Article ID 404928, 26 pages
http://dx.doi.org/10.1155/2012/404928
Research Article

Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential Equations

Xiao-Bao Shu,1 Yongzeng Lai,2 and Fei Xu2

1Department of Mathematics, Hunan University, Changsha 410082, China
2Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5

Received 27 December 2011; Accepted 18 January 2012

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2012 Xiao-Bao Shu et al. 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

By introducing subdifferentiability of lower semicontinuous convex function φ(x(t),x(t−τ)) and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomous neutral nonlinear functional differential equation x″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0, x(0)=0.