Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 140, pp. 1-16.

Title: Almost automorphy for bounded solutions to second-order neutral
       differential equations with piecewise constant arguments
        
Authors: Chuan-Hua Chen (Sichuan Univ., Chengdu, China)
         Hong-Xu Li     (Sichuan Univ., Chengdu, China)

Abstract:
 By introducing the method of decomposition of almost automorphic sequence,
 we give some results on the almost automorphy of bounded solutions for
 the second-order neutral differential equations with piecewise constant
 argument
 $$
 (x(t)+px(t-1))''=qx([t])+f(t),\quad t\in\mathbb{R},
 $$
 where [.] denotes the greatest integer function,
 $p, q$ are nonzero constants, and f(t) is almost automorphic.
 Some examples illustrate our results.

Submitted January 8, 2013. Published June 21, 2013.
Math Subject Classifications: 34K40
Key Words: Almost automorphic; neutral differential equation; bounded solution;
           piecewise constant argument.