Oscillation of Nonlinear Neutral Delay Difference Equations of Fourth Order

This paper focuses on the study of oscillatory behavior fourth-order nonlinear neutral delay difference equations. The authors use mathematical techniques, such as Riccati substitution and comparison technique, to explore regularity existence properties solutions these present a new form equation: Δ(a(m)(Δ3z(m))p1−1)+p(m)wp2−1(σ(m))=0, where z(m)=w(m)+q(m)w(m−τ) with following conditions: ∑s=m0∞1a(1p1−1(s))=∞. equation represents system state at any given time depends its current past values. demonstrate insights into equations conditions required for be well-behaved. They also provide numerical example support their findings.