Oscillation criteria of third order nonlinear neutral difference equations

G.Ayyappan

doi:10.26637/mjm302/013

Abstract

In this paper we consider the third order nonlinear neutral difference equation of the form
$$
\Delta\left(r_n\left(\Delta^2\left(x_n \pm p_n x_{\sigma(n)}\right)\right)^\alpha\right)+f\left(n, x_{\tau(n)}\right)=0,
$$
we establish some sufficient conditions which ensure that every solution of this equation are either oscillatory or converges to zero. Examples are provided to illustrate the main results.

Keywords:

oscillation, neutral difference equations

Mathematics Subject Classification:

39A10

Authors Imprint References Funding Related Articles Downloads

G.Ayyappan Department of Mathematics, Periyar University College of Arts and Science, Mettur Dam-636401, Salem Dt., Tamilnadu, India. https://orcid.org/0000-0002-5608-7032

Pages: 216-223
Date Published: 01-04-2015
Vol. 3 No. 02 (2015): Malaya Journal of Matematik (MJM)

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