Fourth-Order Nonlinear Neutral Difference Equations: Oscillation via New Canonical Transforms

Palani Ganesan; Govindasamy Palani; JohnR. Graef; Ethiraju Thandapani

doi:10.2478/tmmp-2025-0025

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Fourth-Order Nonlinear Neutral Difference Equations: Oscillation via New Canonical Transforms

Tatra Mountains Mathematical Publications

Volume 90 (2025): Issue 2 (December 2025)

By: Palani Ganesan, Govindasamy Palani, JohnR. Graef and Ethiraju Thandapani

Open Access

|Dec 2025

Abstract

This paper presents a new method of transforming fourth-order nonlinear semi-canonical neutral difference equations into canonical type equations. This technique reduces the set of nonoscillatory solutions to only two. By eliminating these two remaining types of nonoscillatory solutions, the authors are able to obtain new criteria for the oscillation of all solutions of the equation under investigation. Examples are provided to demonstrate the significance and novelty of the main results.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0025 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 107 - 122

Submitted on: Oct 3, 2024

Accepted on: Jul 4, 2025

Published on: Dec 18, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

oscillation,

fourth-order,

neutral difference equation,

canonical transform

Related subjects:

Mathematics,

General mathematics

© 2025 Palani Ganesan, Govindasamy Palani, JohnR. Graef, Ethiraju Thandapani, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 90 (2025): Issue 2 (December 2025)