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New oscillation constraints for even-order delay differential equations

Moaaz Osama, Anis Mona, El-Deeb Ahmed A., Elshenhab Ahmed M.

Opuscula Mathematica

2023

Vol. 43, no. 3

455--467

The purpose of this paper is to study the oscillatory properties of solutions to a class of delay differential equations of even order. We focus on criteria that exclude decreasing positive solutions. As in this paper, this type of solution emerges when considering the noncanonical case of even equations. By finding a better estimate of the ratio between the Kneser solution with and without delay, we obtain new constraints that ensure that all solutions to the considered equation oscillate. The new findings improve some previous findings in the literature.

Asymptotic behavior of even-order noncanonical neutral differential equations

Moaaz Osama, Muhib Ali, Abdeljawad Thabet, Santra Shyam S., Anis Mona

Demonstratio Mathematica

2022

Vol. 55, nr 1

28--39

In this article, we study the asymptotic behavior of even-order neutral delay differential equation (a⋅(u+ρ⋅u∘τ)(n−1))′(ℓ)+h(ℓ)u(g(ℓ))=0,ℓ≥ℓ0, where n≥4, and in noncanonical case, that is, ∞∫a−1(s)ds<∞. To the best of our knowledge, most of the previous studies were concerned only with the study of n-order neutral equations in canonical case. By using comparison principle and Riccati transformation technique, we obtain new criteria which ensure that every solution of the studied equation is either oscillatory or converges to zero. Examples are presented to illustrate our new results.