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.

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.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

scholarly journals Asymptotic behavior of nonoscillatory solutions of a higher order functional differential equation

1981 ◽  
Vol 24 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Approach Zero ◽  
Image Position

The asymptotic behavior of nonoscillatory solutions of nth order nonlinear functional differential equationsis investigated. Sufficient conditions are provided which ensure that all nonoscillatory solutions approach zero as t → ∞.

scholarly journals Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
A. T. Ademola ◽  
B. S. Ogundare ◽  
M. O. Ogundiran ◽  
O. A. Adesina
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Third Order ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
Lyapunov’S Second Method ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples.

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 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 Nonoscillation theorems for functional differential equations of arbitrary order

1984 ◽  
Vol 7 (2) ◽  
pp. 249-256 ◽  
Author(s):  
John R. Graef ◽  
Myron K. Grammatikopoulos ◽  
Yuichi Kitamura ◽  
Takasi Kusano ◽  
Hiroshi Onose ◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Arbitrary Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Nonoscillation Theorem

The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.

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.

Properties 𝐴 and 𝐵 of 𝑛th Order Linear Differential Equations with Deviating Argument

1999 ◽  
Vol 6 (6) ◽  
pp. 553-566
Author(s):  
R. Koplatadze ◽  
G. Kvinikadze ◽  
I. P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Order Linear Differential Equation ◽  
Deviating Arguments ◽  
Order Linear ◽  
Deviating Argument ◽  
Linear Differential

Abstract Sufficient conditions for the nth order linear differential equation 𝑢(𝑛) (𝑡) + 𝑝(𝑡)𝑢(τ(𝑡)) = 0, 𝑛 ≥ 2, to have Property 𝐴 or Property 𝐵 are established in both the delayed and the advanced cases. These conditions essentially improve many known results not only for differential equations with deviating arguments but for ordinary differential equations as well.

scholarly journals A nonoscillation theorem for a second order sublinear retarded differential equation

1976 ◽  
Vol 15 (3) ◽  
pp. 401-406 ◽  
Author(s):  
Takaŝi Kusano ◽  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Functional ◽  
Retarded Differential Equation ◽  
All Solutions ◽  
Functional Differential ◽  
Nonoscillation Theorem

Sufficient conditions are obtained for all solutions of a class of second order nonlinear functional differential equations to be nonoscillatory.

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