Positive periodic solution for second-order neutral differential equation with variable delay

Abstract

In this paper, we consider the following second-order neutraldifferential equation with variable delay

$$(x(t)-cx(t-\tau))''+a(t)x(t)=f(t,x(t-\delta(t))),$$

where$|c|\neq1$. By applications of Krasnoselskii's fixed point theorem,some analysis skills and choosing available operators, sufficient conditions for the existence of periodic solution are established.