Conditions for oscillation and convergence of solutions to second order neutral delay difference equations with variable coefficients

A. Murugesan; K. Ammamuthu

doi:10.26637/mjm502/014

Abstract

In this paper, we deals with the second order neutral functional difference equation of the form
$$
\Delta(r(n) \Delta(x(n)-p(n) x(n-\tau)))+q(n) f(x(n-\sigma))=0 ; \quad n \geq n_0
$$
where $\{r(n)\},\{p(n)\}$ and $\{q(n)\}$ 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.

Keywords:

Oscillation, nonoscillation, second order, neutral, delay difference equations

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

A. Murugesan Department of Mathematics, Government Arts College (Autonomous), Salem-636007, Tamil Nadu, India.
K. Ammamuthu Department of Mathematics, Arignar Anna Government Arts College, Attur-636121, Tamil Nadu, India.

Pages: 367-377
Date Published: 01-04-2017
Vol. 5 No. 02 (2017): Malaya Journal of Matematik (MJM)

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