Periodic solutions for nonlinear differential equation with functional delay

Abstract. We use the modification of Krasnoselskii’s fixed point theorem due to T. A. Burton ([3]) to show that the scalar nonlinear differential equa-tion with functional delay x′(t) = −a(t)x3(t) +G(t, x3(t − r(t))) has a periodic solution. It is not required that r(t) be differentiable, while a and G are continuous with respect to their arguments