Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria

Gunasekaran Nithyakala, George E. Chatzarakis (), Govindasamy Ayyappan and Ethiraju Thandapani
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Gunasekaran Nithyakala: Department of Applied Mathematics and Computational Science, Thiagarajar College of Engineering, Madurai 625 015, Tamilnadu, India
George E. Chatzarakis: Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, 15122 Marousi, Athens, Greece
Govindasamy Ayyappan: Department of Mathematics, Government Arts and Science College, Pappireddipatti 636 905, Tamilnadu, India
Ethiraju Thandapani: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamilnadu, India

Mathematics, 2024, vol. 12, issue 18, 1-10

Abstract: The purpose of this paper is to add some new asymptotic and oscillatory results for third-order neutral delay differential equations with noncanonical operators. Without assuming any extra conditions, by using the canonical transform technique, the studied equation is changed to a canonical type equation, and this reduces the number of classes of nonoscillatory solutions into two instead of four. Then, we obtain Myshkis type sufficient conditions for the nonexistence of Kneser type solutions for the studied equation. Finally, employing these newly obtained criteria, we provide conditions for the oscillation of all solutions of the studied equation. Examples are presented to illustrate the importance and the significance of the main results.

Keywords: neutral differential equation; noncanonical; third-order; Kneser solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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