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

Barakah Almarri and Osama Moaaz ()
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Barakah Almarri: Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Osama Moaaz: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Mathematics, 2023, vol. 11, issue 4, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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