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Volume 14
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10.3390/axioms14020091
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform

by
Bose Rani
1,
George E. Chatzarakis
2,* and
Ethiraju Thandapani
3
1
Department of Mathematics, Sri Kanyaka Parameswari Arts and Science College for Women, Chennai 600103, India
2
Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, 15122 Marousi, Greece
3
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(2), 91; https://doi.org/10.3390/axioms14020091
Submission received: 9 December 2024 / Revised: 16 January 2025 / Accepted: 23 January 2025 / Published: 26 January 2025
(This article belongs to the Section Mathematical Analysis)
Versions Notes

Abstract

In this paper, without assuming any extra conditions, the third-order unstable noncaonical advanced differential equation is changed into a canonical form that reduces the number of classes of nonoscillatory solutions into two instead of four. Using comparison and integral averaging method, new sufficient conditions are obtained so that all solutions to have Property B or oscillate. Specific numerical examples are provided to demonstrate the importance and the significance of the main results.
Keywords: oscillation; third-order; noncanonical; unstable type; advanced differential equation oscillation; third-order; noncanonical; unstable type; advanced differential equation

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MDPI and ACS Style

Rani, B.; Chatzarakis, G.E.; Thandapani, E. Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform. Axioms 2025, 14, 91. https://doi.org/10.3390/axioms14020091

AMA Style

Rani B, Chatzarakis GE, Thandapani E. Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform. Axioms. 2025; 14(2):91. https://doi.org/10.3390/axioms14020091

Chicago/Turabian Style

Rani, Bose, George E. Chatzarakis, and Ethiraju Thandapani. 2025. "Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform" Axioms 14, no. 2: 91. https://doi.org/10.3390/axioms14020091

APA Style

Rani, B., Chatzarakis, G. E., & Thandapani, E. (2025). Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform. Axioms, 14(2), 91. https://doi.org/10.3390/axioms14020091

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