Multiplicity results of periodic solutions for systems of first order delay differential equation

This paper is concerned with the periodic solutions of the following delay non-autonomous systems(1)u′(t)=-f(t,u(t-r)),where r > 0, f ∈ C(R1 × Rn, Rn) satisfies f(t + r, z) = f(t, z) for all z ∈ Rn. Some multiplicity results of periodic solutions of (1) are obtained via variational methods.