Oscillatory Properties of Third-order Neutral Delay Difference Equations

Abstract

In this paper, we are connected with oscillation of third-order linear neutral delay difference equation of the form Δ ( c 2 ( σ ) Δ ( c 1 ( σ ) Δ h ( σ ) ) ) + p ( σ ) x ( σ − ς ) = 0 , σ ≥ σ 0 > 0 , where h ( σ ) = x ( σ ) + q ( σ ) x ( σ − η ) . Here c 1(σ) and c 2(σ) are the sequence of positive integers, p(σ) and q(σ) are positive and real sequences such that q(σ) ≥ q 0 > 1 and p(σ) ≠ 0, ς, η are positive integers, such that ς > η.