Second-Order Neutral Differential Equations with Sublinear Neutral Terms: New Criteria for the Oscillation

Meraa Arab, Hajer Zaway, Ali Muhib () and Sayed K. Elagan
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Meraa Arab: Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia
Hajer Zaway: Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia
Ali Muhib: Department of Mathematics, Faculty of Applied and Educational Sciences—Al-Nadera, Ibb University, Ibb 72072, Yemen
Sayed K. Elagan: Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shebin Elkom 32511, Egypt

Mathematics, 2025, vol. 13, issue 6, 1-14

Abstract: This paper aims to study the oscillatory behavior of second-order neutral differential equations. Using the Riccati substitution technique, we introduce new oscillation criteria that essentially improve some related criteria from the literature. We provide some examples and compare the results in this paper with earlier results to illustrate the importance of our results.

Keywords: oscillation criteria; Riccati substitution; canonical case (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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