Oscillation of First Order Neutral Difference Equations

A. Murugesana,* and R. Suganthib

Oscillation of First Order Neutral Difference Equations

Authors :

A. Murugesan^a,* and R. Suganthi^b

Author Address :

^aDepartment of Mathematics, Government Arts College (Autonomous), Salem-636007, Tamil Nadu, India.
^bDepartment of Mathematics, Vysya College, Salem-636103, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we consider a class of first order neutral difference equations of the form
\begin{equation*} \Delta[r(n)(x(n)+p(n)x(n-\tau))]+q(n)x(n-\sigma)=0,\quad n\geq n_0. \quad \quad \quad (*)\end{equation*}
Some sufficient conditions for the oscillation of all solutions of (*) are established. Our result extend and improve some of the previous results in the literature. Some examples are considered to illustrate our results.

Keywords :

Oscillation, nonoscillation, neutral, difference equations.

DOI :

Article Info :

Received : December 22, 2015; Accepted : January 12, 2016.