Oscillation criteria for third order neutral difference equations with distributed delay

R. Arula and G. Ayyappanb,*

Oscillation criteria for third order neutral difference equations with distributed delay

Authors :

R. Arul^a and G. Ayyappan^b,*

Author Address :

^a,bDepartment of Mathematics, Kandaswami Kandar’s College, Velur - 638 182, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper we study the oscillatory behavior of third order neutral difference equation of the form

\be \Delta\Big(r(n) \Delta^2
z(n)\Big)+\sum_{s=c}^{d}q(n,s)f(x(n+s-\sigma))=
0, n\geq n_0\geq 0, \ee 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 (0.1) 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 :

Third order, oscillation, neutral difference equations, Philos - type.

DOI :

Article Info :

Received : January 10, 2013; Accepted : February 12, 2013.