Oscillation criteria for third order neutral difference equations with distributed delay

R. Arul; G. Ayyappan

doi:10.26637/mjm102/001

Abstract

In this paper we study the oscillatory behavior of third order neutral difference equation of the form
$$
\Delta\left(r(n) \Delta^2 z(n)\right)+\sum_{s=c}^d q(n, s) f(x(n+s-\sigma))=0, n \geq n_0 \geq 0,
$$
where $z(n)=x(n)+\sum_{s=a}^b p(n, s) x(n+s-\tau)$. We establish some sufficient conditions which ensure that every solution of the equation oscillates or converges to zero by using a generalized Ricaati transformation and Philos - type technique. An example is given to illustrate the main result.

Keywords:

oscillation, neutral difference equations, Philos - type

Mathematics Subject Classification:

39A10

Authors Imprint References Funding Related Articles Downloads

R. Arul Department of Mathematics, Kandaswami Kandar’s College, Velur - 638 182, Tamil Nadu, India.
G. Ayyappan Department of Mathematics, Kandaswami Kandar’s College, Velur - 638 182, Tamil Nadu, India. https://orcid.org/0000-0002-5608-7032

Pages: 1-10
Date Published: 01-04-2013
Vol. 1 No. 02 (2013): Malaya Journal of Matematik (MJM)

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