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Article

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

1
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
2
Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
3
Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia
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Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
*
Author to whom correspondence should be addressed.
Academic Editors: Aviv Gibali and Calogero Vetro
Symmetry 2021, 13(6), 934; https://doi.org/10.3390/sym13060934
Received: 24 April 2021 / Revised: 17 May 2021 / Accepted: 20 May 2021 / Published: 25 May 2021
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. View Full-Text
Keywords: oscillation; non-oscillation; nonlinear; delay argument; canonical; impulse; non-canonical oscillation; non-oscillation; nonlinear; delay argument; canonical; impulse; non-canonical
MDPI and ACS Style

Santra, S.S.; Khedher, K.M.; Nonlaopon, K.; Ahmad, H. New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions. Symmetry 2021, 13, 934. https://doi.org/10.3390/sym13060934

AMA Style

Santra SS, Khedher KM, Nonlaopon K, Ahmad H. New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions. Symmetry. 2021; 13(6):934. https://doi.org/10.3390/sym13060934

Chicago/Turabian Style

Santra, Shyam Sundar, Khaled Mohamed Khedher, Kamsing Nonlaopon, and Hijaz Ahmad. 2021. "New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions" Symmetry 13, no. 6: 934. https://doi.org/10.3390/sym13060934

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