Electron. J. Diff. Equ., Vol. 2013 (2013), No. 140, pp. 1-16.

Almost automorphy for bounded solutions to second-order neutral differential equations with piecewise constant arguments

Chuan-Hua Chen, Hong-Xu Li

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.

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Chuan-Hua Chen
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: chenchuanhua8@163.com
Hong-Xu Li
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: hoxuli@sina.com

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