Conditions for Oscillation and Convergence of Solutions to Second Order Neutral Delay Difference Equations with Variable Coefficients

A. Murugesan1,* and K. Ammamuthu2

Conditions for Oscillation and Convergence of Solutions to Second Order Neutral Delay Difference Equations with Variable Coefficients

Authors :

A. Murugesan^1,* and K. Ammamuthu²

Author Address :

¹Department of Mathematics, Government Arts College (Autonomous), Salem-636007, Tamil Nadu, India.
²Department of Mathematics, Arignar Anna Government Arts College, Attur-636121, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we deals with the second order neutral functional difference equation of the form \begin{equation*}\Delta \left(r(n)\Delta (x(n)-p(n)x(n-\tau))\right)+q(n)f(x(n-\sigma))=0;\quad n\geq n_0 \quad (*) \end{equation*} where $\left\{r(n)\right\}$, $\left\{p(n)\right\}$ and $\left\{q(n)\right\}$ are sequences of real numbers, $\tau$ and $\sigma$ are positive integers and $f:R\rightarrow R$ is a real valued function. We determine sufficient conditions under which every solutions of $(*)$ is either oscillatory or tends to zero.