Theorems on oscillatory and asymptotic behavior of second order nonlinear neutral difference equations

A. Murugesan; K. Venkataramanan

doi:10.26637/MJM0504/0002

Abstract

In this paper, we discuss a class of second order neutral delay difference equation of the form
$\Delta\left[r(n)|\Delta z(n)|^{\alpha-1} \Delta z(n)\right]+q(n) f(x(n-\sigma))=0 ; \quad n \geq n_0$
where $z(n)=x(n)-p(n) x(n-\tau)$. We determine sufficient conditions under which every solution of the given system is either oscillatory or tends to zero. Our results improve a number of related results reported in the literature.

Keywords:

Oscillation, nonoscillation, asymptotic behavior, neutral, second order, difference equation

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. Venkataramanan Department of Mathematics, Vysya College, Salem-636103, Tamil Nadu, India.

Pages: 619-624
Date Published: 01-10-2017
Vol. 5 No. 04 (2017): Malaya Journal of Matematik (MJM)

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