scholarly journals Nonoscillation of First Order Impulse Differential Equations with Delay

1997 ◽  
Vol 206 (1) ◽  
pp. 254-269 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Michael Drakhlin
Keyword(s):  
Differential Equations ◽  
First Order ◽  
Equations With Delay

scholarly journals New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 454 ◽  
Author(s):  
Osama Moaaz ◽  
Shigeru Furuichi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Differential Inequalities ◽  
Neutral Differential Equations ◽  
First Order ◽  
A New Technique ◽  
Equations With Delay ◽  
Higher Order Differential Equations ◽  
First Order Differential Equations

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

scholarly journals Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 650
Author(s):  
Ahmed AlGhamdi ◽  
Clemente Cesarano ◽  
Barakah Almarri ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
First Order ◽  
Main Equation ◽  
Engineering Physics ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Oscillatory Properties

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. The purpose of this article is to explore the oscillation of fourth-order differential equations with delay arguments. New Kamenev-type oscillatory properties are established, which are based on a suitable Riccati method to reduce the main equation into a first-order inequality. Our new results extend and simplify existing results in the previous studies. Examples are presented in order to clarify the main results.

scholarly journals The Existence and Application of Unbounded Connected Components

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hua Luo ◽  
Ruyun Ma
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Connected Components ◽  
Global Behavior ◽  
Positive Periodic Solutions ◽  
First Order ◽  
Physiological Processes ◽  
Equations With Delay ◽  
First Order Differential Equations

LetXbe a Banach space andCna family of connected subsets ofR×X. We prove the existence of unbounded components in superior limit of{Cn}, denoted bylim¯ Cn, which have prescribed shapes. As applications, we investigate the global behavior of the set of positive periodic solutions to nonlinear first-order differential equations with delay, which can be used for modeling physiological processes.

scholarly journals Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method

2021 ◽  
Vol 53 ◽  
Author(s):  
Akmal Raza ◽  
Arshad Khan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Singularly Perturbed ◽  
First Order ◽  
Wavelet Collocation Method ◽  
Fitted Operator ◽  
Equations With Delay

An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then  solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly  to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11], [28].

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