Abstract and Applied Analysis
Volume 2012 (2012), Article ID 186361, 10 pages
http://dx.doi.org/10.1155/2012/186361
Research Article

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

Rong-Kun Zhuang

Department of Mathematics, Huizhou University, Huizhou 516007, China

Received 12 November 2011; Accepted 12 December 2011

Academic Editor: Simeon Reich

Copyright © 2012 Rong-Kun Zhuang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 ( 𝑥 ( 𝑡 ) + 𝑝 𝑥 ( 𝑡 − 1 ) ) ( 𝑁 ) = 𝑞 𝑥 ( [ 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.