This analysis establishes criteria for oscillation in third-order delay differential equations, indicating broader applications in differential equation theory.
In this work, we adopted an approach similar to that of Chatzarakis’, by transforming the oscillation analysis of third-order differential equations into an equivalent first-order problem. A key generalization in our study is the extension coefficient b(t) from the range 0≤b(t)≤1 to b(t)≥1. Moreover, we established several oscillation criteria applicable to the canonical and non-canonical cases. Our conclusions complement and extend the oscillation theory for third-order delay differential equations. Several examples are provided to illustrate our results.
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Guo et al. (2025) studied this question.
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