Abstract
In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.
Highlights
The study of delay differential equations is a very active area of research since it is much richer than the corresponding theory of ordinary differential equations
We highlight some current developments in oscillation theory for second-order neutral differential equations
For more details on the oscillation theory for second-order neutral differential equations, we refer the reader to the papers [19,20,21,22,23,24,25]
Summary
The study of delay differential equations is a very active area of research since it is much richer than the corresponding theory of ordinary differential equations. In another paper [8], Santra et al considered the secondorder delay differential equations with sub-linear neutral coefficients of the form: distributed under the terms and conditions of the Creative Commons. In a recent paper [9], Santra et al established some new oscillation theorems for the differential equations of the neutral type with mixed delays under the canonical operator with 0 ≤ q < 1. For more details on the oscillation theory for second-order neutral differential equations, we refer the reader to the papers [19,20,21,22,23,24,25]. In this study, we established both sufficient and necessary conditions for the oscillation of second-order differential equations of the form: p(θ ) g0 (θ ).
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