Existence of Almost Periodic Solutions to N th-Order Neutral Differential Equations with Piecewise Constant Arguments

Abstract

We present some conditions for the existence and uniqueness of almost periodic solutions of $N$th-order neutral differential equations with piecewise constant arguments of the form ${\left(x\left(t\right)+px\left(t-1\right)\right)}^{\left(N\right)}=qx\left(\left[t\right]\right)+f\left(t\right)$, here $[\cdot ]$ is the greatest integer function, $p$ and $q$ are nonzero constants, $N$ is a positive integer, and $f\left(t\right)$ is almost periodic.