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

This paper is concerned with the periodic boundary value problem (1) { u ( t ) + λ u ( t − τ ) = ∇ F ( t , u ( t − τ ) ) a.e. t ∈ [ 0 , 2 τ ] u ( 0 ) − u ( 2 τ ) = u ( 0 ) − u ( 2 τ ) = 0 , where τ > 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.