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.