## Journal of Applied Mathematics

### Convergence and Divergence of the Solutions of a Neutral Difference Equation

#### Abstract

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form $\Delta [x(n)+cx(\tau (n))]+p(n)x(\sigma (n))=0$, where $\tau (n)$ is a general retarded argument, $\sigma (n)$ is a general deviated argument (retarded or advanced), $c\in R$, ${(p(n))}_{n\ge 0}$ is a sequence of positive real numbers such that $p(n)\ge p$, $p\in {R}_{+}$, and $\Delta$ denotes the forward difference operator $\Delta x(n)=x(n+1)-x(n)$. Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to cc.

#### Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 262316, 18 pages.

Dates
First available in Project Euclid: 15 March 2012

https://projecteuclid.org/euclid.jam/1331818651

Digital Object Identifier
doi:10.1155/2011/262316

Mathematical Reviews number (MathSciNet)
MR2846437

Zentralblatt MATH identifier
1235.39005

#### Citation

Chatzarakis, G. E.; Miliaras, G. N. Convergence and Divergence of the Solutions of a Neutral Difference Equation. J. Appl. Math. 2011 (2011), Article ID 262316, 18 pages. doi:10.1155/2011/262316. https://projecteuclid.org/euclid.jam/1331818651