Oscillation Criteria of Solutions of Fourth-Order Neutral Differential Equations

Alanoud Almutairi,M A Aiyashi,Barakah Almarri,Kamsing Nonlaopon,Omar Bazighifan

doi:10.3390/fractalfract5040155

Abstract

In this paper, we study the oscillation of solutions of fourth-order neutral delay differential equations in non-canonical form. By using Riccati transformation, we establish some new oscillation conditions. We provide some examples to examine the applicability of our results.

Highlights

In this work, we obtain some oscillation conditions of equation10.3390/fractalfract5040155Academic Editors: Burcu Gürbüz and Arran Fernandez b(t) y000 (t) α 0 j+ ∑ νi (t) x α ( gi (t)) = 0. (1) i =1Received: 10 September 2021 where j is a positive integer and Accepted: 2 October 2021Published: 7 October 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in y(t) = x (t) + β(t) x (z(t)). (2)
In this work, we study the oscillatory behavior of solutions of the fourth-order neutral delay differential equations in noncanonical form
Equation (1) into a first-order equation, while in our article, we discuss the oscillation and asymptotic properties of differential equations in a noncanonical form of the neutral-type, and we employ a different approach based on using the Riccati technique to reduce the main equation into a first-order inequality to obtain more effective oscillation conditions for Equation (1)

Summary

Introduction

2021, 5, 155 find application in explaining human self-balancing With regard to their practical importance, oscillation of fourth-order neutral differential equations has been studied extensively during recent decades, see [3,4,5,6,7,8,9]. There are many studies on the oscillatory properties of different orders of some differential equations in noncanonical form, see [15,16,17,18,19,20,21,22,23,24,25]. In this work, we study the oscillatory behavior of solutions of the fourth-order neutral delay differential equations in noncanonical form. To the best of our knowledge, only a few papers have studied the oscillation and qualitative behavior of fourth-order neutral delay differential equations in noncanonical form

Mathematical Background

Oscillation Criteria

Conclusions