Our aim in this paper is to give some new results on the oscillatory behavior of all solutions of the delay difference inequalities x(n) { Lmx(n)+a(n)x(n)+(q(n)+ p j(n))x[n−mτ] } ≤ 0 for m odd

Pon.Sundar 1 and B.Kishokkumar 2 1 Department of Mathematics, Om Muruga College of Arts & Science, Mettur, Tamilnadu, India. Email: mydt972009@gmail.com 2 Department of Mathematics, Paavai Engineering College, Namakkal, Tamilnadu, India. Email: bkishok@gmail.com __________________________________________________________________________________ Abstract: In this article, we use the Riccati transformation technique and some inequalities, to establish oscillation theorems for all solutions to even-order quasilinear neutral difference equation     0 1 0, = ) ( ) ( )) ( ( ) ( ) ( n n n x n q n x n p n x m          