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

Abstract

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