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

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)