scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

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.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

scholarly journals New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1159
Author(s):  
Shyam Sundar Santra ◽  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Fluid Dynamics ◽  
Neural Networks ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Delay Differential

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

scholarly journals On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 134 ◽  
Author(s):  
Shyam Sundar Santra ◽  
Ioannis Dassios ◽  
Tanusri Ghosh
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Second Order ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Non Linear ◽  
Delay Differential

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

scholarly journals New Aspects for Oscillation of Differential Systems with Mixed Delays and Impulses

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 780
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Shao-Wen Yao
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Necessary Conditions ◽  
Second Order ◽  
Mixed Delays ◽  
Differential Systems ◽  
Second Order Differential Equation ◽  
Sufficient And Necessary Conditions ◽  
Engineering Physics

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. In this work, we obtain sufficient and necessary conditions for the oscillation of the solutions to a second-order differential equation with impulses and mixed delays when the neutral coefficient lies within [0,1). Furthermore, an examination of the validity of the proposed criteria has been demonstrated via particular examples.

scholarly journals More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 986
Author(s):  
Osama Moaaz ◽  
Mona Anis ◽  
Dumitru Baleanu ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
New Criteria ◽  
Oscillation Of Solutions

The motivation for this paper is to create new criteria for oscillation of solutions of second-order nonlinear neutral differential equations. In more than one respect, our results improve several related ones in the literature. As proof of the effectiveness of the new criteria, we offer more than one practical example.

scholarly journals New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1111
Author(s):  
Shyam Sundar Santra ◽  
Abhay Kumar Sethi ◽  
Osama Moaaz ◽  
Khaled Mohamed Khedher ◽  
Shao-Wen Yao
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Theorems

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

scholarly journals New Theorems for Oscillations to Differential Equations with Mixed Delays

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 367
Author(s):  
Shyam Sundar Santra ◽  
Debasish Majumder ◽  
Rupak Bhattacharjee ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
...  
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Mixed Delays ◽  
Second Order Differential Equations ◽  
Neutral Term ◽  
The Right ◽  
Necessary And Sufficient

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form p(ι)w′(ι)α′+r(ι)uβ(ν(ι))=0,ι≥ι0 where w(ι)=u(ι)+q(ι)u(ζ(ι)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Sign in / Sign up

Export Citation Format

Share Document