Simplified and improved criteria for oscillation of delay differential equations of fourth order

O Moaaz,E E Mahmoud,A Muhib,W Alharbi,D Baleanu

doi:10.1186/s13662-021-03449-y

Abstract

An interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples.

Highlights

Introduction and preliminariesDelay differential equations (DDEs) are of great importance in modeling many phenomena and problems in various applied sciences, see [13]
One can trace the evolution in the study of the oscillatory properties of higher-order DDEs with noncanonical operator through works of Baculikova et al [7], Zhang et al [23,24,25], and, recently, Moaaz et al [16, 18]
This study is concerned with finding sufficient oscillation conditions for the solutions of the DDE

Summary

Introduction

Introduction and preliminariesDelay differential equations (DDEs) are of great importance in modeling many phenomena and problems in various applied sciences, see [13]. The mounting interest in studying the qualitative properties of solutions of DDEs is easy to notice, see for example [1,2,3,4,5,6,7,8,9,10,11,12] and [14,15,16,17,18,19,20,21,22,23,24,25]. The equations with noncanonical operator did not receive the same attention as the equations in the canonical case. One can trace the evolution in the study of the oscillatory properties of higher-order DDEs with noncanonical operator through works of Baculikova et al [7], Zhang et al [23,24,25], and, recently, Moaaz et al [16, 18].

Objectives

Conclusion