Multiplicity results of periodic solutions for a class of second order delay differential systems

This paper is concerned with the periodic boundary value problem equation(1){ü(t)+λu(t−τ)=∇F(t,u(t−τ))a.e. t∈[0,2τ]u(0)−u(2τ)=u̇(0)−u̇(2τ)=0, where τ>0τ>0 is a given constant, λ∈R is a parameter. The variational principle is given and some multiplicity results of periodic solutions of (1) are obtained directly via variational methods.