On Almost Automorphic Solutions of Third-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

Abstract

We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form $$(x(t) + px(t − 1))′′′ = a_0x([t]) + a_1x([t − 1]) + f(t),$$ where [·] is the greatest integer function, $p,$ $a_0$ and $a_1$ are nonzero constants, and $f(t)$ is almost automorphic.