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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.

Mannheim curves and their partner curves in Minkowski 3-space E13

Elsharkawy Ayman, Elshenhab Ahmed M.

Demonstratio Mathematica

2022

Vol. 55, nr 1

798--811

The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski 3-space. Some characterizations according to the curvatures and torsions of the curves are given. Finally, some relations under the conditions for Mannheim curves and their partner curves to be generalized helices are presented. All the possible cases for the partner curves to be spacelike and timelike are considered in the whole of the article.