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
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).