Periodic solutions of first-order nonlinear functional differential equations

In this paper, we obtain a set of “easily verifiable” sufficient conditions for the existence of the periodic solutions of the first-order linear functional differential equations with periodic perturbation x′(t)=l(x)(t)+f(t,xt),x′(t)=l(x)(t)+f(t,xt), where l:C(R)→C(R) is a linear bounded operator. These conditions generalize and improve the known results given in the literature.