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.

Keywords

• fixed point
• large contraction
• periodic solution
• totally nonlinear neutral equation