## Abstract and Applied Analysis

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

Rong-Kun Zhuang

#### 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 ${(x(t)+px(t-1))}^{(N)}=qx([t])+f(t)$, here $[\cdot ]$ is the greatest integer function, $p$ and $q$ are nonzero constants, $N$ is a positive integer, and $f(t)$ is almost periodic.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 186361, 10 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495642

Digital Object Identifier
doi:10.1155/2012/186361

Mathematical Reviews number (MathSciNet)
MR2889077

Zentralblatt MATH identifier
1243.34103

#### Citation

Zhuang, Rong-Kun. Existence of Almost Periodic Solutions to $N$ th-Order Neutral Differential Equations with Piecewise Constant Arguments. Abstr. Appl. Anal. 2012 (2012), Article ID 186361, 10 pages. doi:10.1155/2012/186361. https://projecteuclid.org/euclid.aaa/1355495642

#### References

• R. Yuan, “The existence of almost periodic solutions to two-dimensional neutral differential equations with piecewise constant argument,” Scientia Sinica A, vol. 27, no. 10, pp. 873–881, 1997.
• Z. Li and M. He, “The existence of almost periodic solutions of second order neutral differential equations with piecewise constant argument,” Northeastern Mathematical Journal, vol. 15, no. 3, pp. 369–378, 1999.
• G. Seifert, “Second-order neutral delay-differential equations with piecewise constant time dependence,” Journal of Mathematical Analysis and Applications, vol. 281, no. 1, pp. 1–9, 2003.
• R. Yuan, “A new almost periodic type of solutions of second order neutral delay differential equations with piecewise constant argument,” Science in China. Series A, vol. 43, no. 4, pp. 371–383, 2000.
• R. Yuan, “Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument,” Nonlinear Analysis. Theory, Methods & Applications, vol. 41, pp. 871–890, 2000.
• K. L. Cooke and J. Wiener, “A survey of differential equations with piecewise continuous arguments,” in Delay Differential Equations and Dynamical Systems, vol. 1475, pp. 1–15, Springer, Berlin, Germany, 1991.
• A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974.