Oscillation Conditions for Third-Order Delay Differential Equations with Neutral-Type Term

Rongrong Guo () and Haifeng Tian
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Rongrong Guo: Department of General Education, Wuxi University, Wuxi 214105, China
Haifeng Tian: Department of General Education, Wuxi University, Wuxi 214105, China

Mathematics, 2025, vol. 13, issue 22, 1-14

Abstract: 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.

Keywords: delay differential equations; third order; neutral equation; oscillation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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