Advances in Difference Equations
Volume 2009 (2009), Article ID 143175, 14 pages
doi:10.1155/2009/143175
Research Article

On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument

Li Wang and Chuanyi Zhang

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 16 December 2008; Accepted 10 April 2009

Academic Editor: Ondrej Dosly

Copyright © 2009 Li Wang and Chuanyi Zhang. 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

The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argument (EPCA, for short) of the form (x(t)+px(t-1))′′=qx(2[(t+1)/2])+f(t) is considered. The main result obtained in this paper is different from that given by some authors for ordinary differential equations (ODE, for short) and clearly shows the differences between ODE and EPCA. Moreover, it is also different from that given for equation (x(t)+px(t-1))′′=qx([t])+f(t) because of the difference between [t] and 2[(t+1)/2].