N. Prabaharan, John R. Graef, and E. Thandapani
Fourth Order Strongly Noncanonical Neutral Difference Equations: New Oscillation Results
Dynamic Systems and Applications 34 (2025)  83-98

https://doi.org/10.46719/dsa2025.34.04

ABSTRACT.
The authors study the oscillatory behavior of the fourth-order neutral delay difference equation

Δ(m₃(ℓ)Δ(m₂(ℓ)Δ(m₁ℓ)Δz(ℓ)))) + q(ℓ)f(y(ℓ − τ )) = 0

where z(ℓ) = y(ℓ) + p(ℓ)y(ℓ − σ), under the conditions that ∑ m^-1_j(s)  < ꝏ, ℓ varies from ℓ_o to ꝏ, j = 1, 2, 3. New oscillation criteria are obtained with relatively few conditions. The results established are new to the literature as is shown through some examples.

AMS (MOS) Subject Classification. 39A10.

Key Words and Phrases. Oscillation, neutral, fourth-order difference equation, noncanonical
form.