scholarly journals Instability of a Fifth-Order Nonlinear Vector Delay Differential Equation with Multiple Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Zero Solution ◽  
Functional Approach ◽  
Previous Literature ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
Nonlinear Vector ◽  
Delay Differential ◽  
Fifth Order

We study a fifth-order nonlinear vector delay differential equation with multiple deviating arguments. Some criteria for guaranteeing the instability of zero solution of the equation are given by using the Lyapunov-Krasovskii functional approach. Comparing with the previous literature, our result is new and complements some known results.

scholarly journals An instability theorem for a certain fifth-order delay differential equation

Filomat ◽  
2011 ◽  
Vol 25 (3) ◽  
pp. 145-151 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Delay Differential Equation ◽  
Functional Approach ◽  
Constant Delay ◽  
Order Nonlinear Differential Equation ◽  
Delay Differential ◽  
Fifth Order

The main purpose of this paper is to introduce a new instability theorem related to a fifth order nonlinear differential equation with a constant delay. By means of the Lyapunov-Krasovskii ([8], [13]) functional approach, we obtain a new result on the topic.

scholarly journals Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Cemil Tunç ◽  
Melek Gözen
Keyword(s):  
Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Functional Approach ◽  
Third Order ◽  
Deviating Arguments ◽  
The Third ◽  
Multiple Deviating Arguments ◽  
Functional Differential

We consider a nonautonomous functional differential equation of the third order with multiple deviating arguments. Using the Lyapunov-Krasovskiì functional approach, we give certain sufficient conditions to guarantee the asymptotic stability and uniform boundedness of the solutions.

scholarly journals New Oscillation Results for Second-Order Neutral Differential Equations with Deviating Arguments

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1937
Author(s):  
Yakun Wang ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Delay Differential ◽  
The Right

In this paper, we focus on the second-order neutral differential equations with deviating arguments which are under the canonical condition. New oscillation criteria are established, which are based on a first-order delay differential equation and generalized Riccati transformations. The idea of symmetry is a useful tool, not only guiding us in the right way to study this function but also simplifies our proof. Our results are generalizations of some previous results and we provide an example to illustrate the main results.

scholarly journals Instability in Multi Delay Functional Differential Equations of Fourth Order

2015 ◽  
Vol 55 (1) ◽  
pp. 189-198
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
The Subject ◽  
Functional Differential

AbstractA vector functional differential equation of the fourth order with multiple deviating arguments is considered. New sufficient conditions are established to guarantee the instability of the zero solution of the equation to be considered. We give an example to illustrate the subject.

scholarly journals Global attractivity of a class of delay differential equations with impulses

2003 ◽  
Vol 45 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Yuji Liu ◽  
Binggen Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

AbstractIn this paper, we study the global attractivity of the zero solution of a particular impulsive delay differential equation. Some sufficient conditions that guarantee every solution of the equation converges to zero are obtained.

scholarly journals A Stability Result for the Solutions of a Certain System of Fourth-Order Delay Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
A. M. A. Abou-El-Ela ◽  
A. I. Sadek ◽  
A. M. Mahmoud ◽  
R. O. A. Taie
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Delay Differential Equation ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Stability Result ◽  
Zero Solution ◽  
Uniform Stability ◽  
Delay Differential

The main purpose of this work is to give sufficient conditions for the uniform stability of the zero solution of a certain fourth-order vector delay differential equation of the following form:X(4)+F(X˙,X¨)X⃛+Φ(X¨)+G(X˙(t-r))+H(X(t-r))=0.By constructing a Lyapunov functional, we obtained the result of stability.

scholarly journals On the Unstable Solutions to Functional Vector Differential Equations of the Seventh Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Deviating Arguments ◽  
Nonlinear Functional ◽  
Multiple Deviating Arguments ◽  
Seventh Order ◽  
Unstable Solutions ◽  
Vector Differential Equation

This paper studies the instability of the zero solution for a certain nonlinear functional vector differential equation of the seventh order with multiple deviating arguments. Under sufficient conditions, we prove a result on the instability of the zero solution. This work contributes and complements to previously known results in the literature.

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