Oscillation of Second Order Nonlinear Impulsive Neutral Differential Equations

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
A. K. Tripathy ◽  
G. N. Chhatria
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Impulsive Neutral Differential Equations

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 Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

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 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 Amended oscillation criteria for second-order neutral differential equations with damping term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Osama Moaaz ◽  
George E. Chatzarakis ◽  
Thabet Abdeljawad ◽  
Clemente Cesarano ◽  
Amany Nabih
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Application Area ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

Abstract The aim of this work is to improve the oscillation results for second-order neutral differential equations with damping term. We consider the noncanonical case which always leads to two independent conditions for oscillation. We are working to improve related results by simplifying the conditions, based on taking a different approach that leads to one condition. Moreover, we obtain different forms of conditions to expand the application area. An example is also given to demonstrate the applicability and strength of the obtained conditions over known ones.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

scholarly journals Bounded Oscillation Theorem for Unstable-type Neutral Impulsive Differential Equations of the Second Order

2019 ◽  
pp. 1-9
Author(s):  
U. A. Abasiekwere ◽  
E. Eteng ◽  
I. O. Isaac ◽  
Z. Lipcsey
Keyword(s):  
Differential Equations ◽  
Transmission Lines ◽  
High Speed ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Central Place ◽  
Oscillatory Solution ◽  
Second Order ◽  
Oscillation Theorem ◽  
Neutral Differential Equations

The oscillations theory of neutral impulsive differential equations is gradually occupying a central place among the theories of oscillations of impulsive differential equations. This could be due to the fact that neutral impulsive differential equations plays fundamental and significant roles in the present drive to further develop information technology. Indeed, neutral differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits).   In this paper, we study the behaviour of solutions of a certain class of second-order linear neutral differential equations with impulsive constant jumps.  This type of equation in practice is always known to have an unbounded non-oscillatory solution.  We, therefore, seek sufficient conditions for which all bounded solutions are oscillatory and provide an example to demonstrate the applicability of the abstract result.

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