*Article* **Improved Properties of Positive Solutions of Higher Order Differential Equations and Their Applications in Oscillation Theory**

**Barakah Almarri <sup>1</sup> and Osama Moaaz 2,3,\***


**Abstract:** In this article, we present new criteria for testing the oscillation of solutions of higher-order neutral delay differential equation. By deriving new monotonic properties of a class of the positive solutions of the studied equation, we establish better criteria for oscillation. Furthermore, we improve these properties by giving them an iterative character, allowing us to apply the criteria more than once. The results obtained in this paper are characterized by the fact that they do not require the existence of unknown functions and do not need the commutation condition to composition of the delay functions, which are necessary conditions for the previous related results.

**Keywords:** neutral differential equations; higher-order; oscillation theory; monotonic properties; noncanonical case

**MSC:** 34C10; 34K11

**Citation:** Almarri, B.; Moaaz, O. Improved Properties of Positive Solutions of Higher Order Differential Equations and Their Applications in Oscillation Theory. *Mathematics* **2023**, *11*, 924. https:// doi.org/10.3390/math11040924

Academic Editor: Alexandra Kashchenko

Received: 3 January 2023 Revised: 1 February 2023 Accepted: 8 February 2023 Published: 11 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
