scholarly journals Second‐order impulsive differential systems with mixed delays: Oscillation theorems

2021 ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Ioannis Dassios
Keyword(s):  
Second Order ◽  
Mixed Delays ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Oscillation Theorems

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

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

scholarly journals New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 934
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Kamsing Nonlaopon ◽  
Hijaz Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Discrete Equation ◽  
Qualitative Behavior ◽  
Differential Systems ◽  
Impulsive Differential Systems

The oscillation of impulsive 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 impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

On controllability of second order nonlinear impulsive differential systems

2009 ◽  
Vol 71 (1-2) ◽  
pp. 45-52 ◽  
Author(s):  
R. Sakthivel ◽  
N.I. Mahmudov ◽  
J.H. Kim
Keyword(s):  
Second Order ◽  
Differential Systems ◽  
Impulsive Differential Systems

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.

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