Oscillation and Asymptotic Behavior of Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities

Balakrishnan Sudha, George E. Chatzarakis () and Ethiraju Thandapani
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Balakrishnan Sudha: Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur 600203, India
George E. Chatzarakis: Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, 15122 Marousi, Athens, Greece
Ethiraju Thandapani: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India

Mathematics, 2025, vol. 13, issue 5, 1-14

Abstract: In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying the arithmetic–geometric mean inequality along with the linearization method and then using comparison method as well as the integral averaging technique. Finally, we show the importance and novelty of the main results by applying them to special cases of the studied equation.

Keywords: oscillation; third-order; neutral differential equation; mixed nonlinearities; arithmetic–geometric inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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