Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay

Abstract

We use a variant of Krasnoselskii’s fixed point theorem by T.A. Burton to show that the nonlinear neutral differential equation with functional delay $x'(t) = -a(t)h(x(t)) +c(t)x'(t-g(t)) + q(t,x(t) x(t-g(t)))$ has a periodic solution.