On the Stability of Certain Second Order Differential Equations

1964 ◽  
Vol 12 (1) ◽  
pp. 58-59 ◽  
Author(s):  
Harry Hochstadt
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
The Stability

scholarly journals Hyers–Ulam stability of second-order differential equations using Mahgoub transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antony Raj Aruldass ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
New Method ◽  
Ulam Stability ◽  
Second Order Differential Equations ◽  
The Stability

AbstractThe aim of this research is investigating the Hyers–Ulam stability of second-order differential equations. We introduce a new method of investigation for the stability of differential equations by using the Mahgoub transform. This is the first attempt of the investigation of Hyers–Ulam stability by using Mahgoub transform. We deal with both homogeneous and nonhomogeneous second-order differential equations.

Dynamic Stability of a Pendulous Missile Suspension System

1962 ◽  
Vol 29 (2) ◽  
pp. 276-282
Author(s):  
V. Chobotov
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Periodic Coefficient ◽  
Suspension System ◽  
Second Order ◽  
Stability Criteria ◽  
Parametrically Excited ◽  
Second Order Differential Equations ◽  
The Stability

The stability criteria for a missile on a pendulous support are derived for the case of parametrically excited motions of the support. The suspension system is described by two linear second-order differential equations with a periodic coefficient. The analysis is carried out by means of the first method of Liapunov. The results are somewhat modified, however, to obtain greater generality without which the technique is too laborious to be useful.

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.

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 Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

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.

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