International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2689-2702
doi:10.1155/IJMMS.2005.2689

Multiple periodic solutions to a class of second-order nonlinear mixed-type functional differential equations

Xiao-Bao Shu1 and Yuan-Tong Xu2

1Department of Mathematics, Hunan University, Changsha 410082, China
2Department of Mathematics, Zhongshan University, Guangzhou 510275, China

Received 22 October 2004; Revised 23 August 2005

Copyright © 2005 Xiao-Bao Shu and Yuan-Tong Xu. 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 means of variational structure and Z2 group index theory, we obtain multiple periodic solutions to a class of second-order mixed-type differential equations x''(t−τ)+f(t,x(t),x(t−τ),x(t−2τ))=0 and x''(t−τ)+λ(t)f1(t,x(t),x(t−τ),x(t−2τ))=x(t−τ).