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Research Article | Open Access

Improved results for testing the oscillation of functional differential equations with multiple delays

Amira Essam1Osama Moaaz2,3( )Moutaz Ramadan1Ghada AlNemer4Ibrahim M. Hanafy1
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia
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Abstract

In this article, we test whether solutions of second-order delay functional differential equations oscillate. The considered equation is a general case of several important equations, such as the linear, half-linear, and Emden-Fowler equations. We can construct strict criteria by inferring new qualities from the positive solutions to the problem under study. Furthermore, we can incrementally enhance these characteristics. We can use the criteria more than once if they are unsuccessful the first time thanks to their iterative nature. Sharp criteria were obtained with only one condition that guarantees the oscillation of the equation in the canonical and noncanonical forms. Our oscillation results effectively extend, complete, and simplify several related ones in the literature. An example was given to show the significance of the main results.

CLC number: 34C10, 34K11

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AIMS Mathematics
Pages 28051-28070

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Cite this article:
Essam A, Moaaz O, Ramadan M, et al. Improved results for testing the oscillation of functional differential equations with multiple delays. AIMS Mathematics, 2023, 8(11): 28051-28070. https://doi.org/10.3934/math.20231435

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Received: 09 May 2023
Revised: 23 August 2023
Accepted: 24 September 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)