K. S. Vidhyaa, E. Chandrasekaran, John R. Graef, and E. Thandapani
Half-Linear Third-Order Noncanonical Delay Difference Equations: Oscillation via a Semi-Canonical Transform
Dynamic Systems and Applications 34 (2025)   132-149

https://doi.org/10.46719/dsa2025.34.07

ABSTRACT.
In this paper, the authors derive some new criteria for the oscillation of half-linear third-order noncanonical delay difference equations. The results are obtained by first reducing the noncanonical equation into semi-canonical form. This approach reduces the set of possible nonoscillatory solutions into three classes without adding any extra conditions. Then by applying the summation averaging method and a Riccati transformation technique, they obtain new criteria for the oscillation of all solutions. Four examples illustrating the main results are provided.

AMS (MOS) Subject Classification. 39A10.

Key Words and Phrases. Half-linear, third-order, delay difference equation, noncanonical, oscillation.