Multiplicity results of periodic solutions for systems of first order delay differential equation (Q654645)

By applying variational methods, the authors establish existence and multiplicity results for periodic solutions of the non-autonomous delay differential equation \[ u'(t)=-f(t,u(t-r)) \] with \(r>0\) and \(f\in C(\mathbb R^1\times \mathbb R^n,\mathbb R^n)\) satisfying \(f(t+r,z)=f(t,z)\) for all \(z\in \mathbb R^n\).