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 Kamenev-Type Asymptotic Criterion of Fourth-Order Delay Differential Equation

2020 ◽  
Vol 4 (1) ◽  
pp. 7 ◽  
Author(s):  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Delay Differential Equation ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Type Oscillation ◽  
Fourth Order Differential Equation

In this paper, we obtain necessary and sufficient conditions for a Kamenev-type oscillation criterion of a fourth order differential equation of the form r 3 t r 2 t r 1 t y ′ t ′ ′ ′ + q t f y σ t = 0 , where t ≥ t 0 . The results presented here complement some of the known results reported in the literature. Moreover, the importance of the obtained conditions is illustrated via some examples.

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 On stability and boundedness of solutions of a certain fourth-order delay differential equation

1989 ◽  
Vol 12 (3) ◽  
pp. 589-602 ◽  
Author(s):  
Emmanuel O. Okoronkwo
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Delay Differential Equation ◽  
Order Differential Equation ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Delay System ◽  
Boundedness Of Solutions ◽  
Uniform Asymptotic Stability ◽  
Delay Differential

Using a Razumikhin - type theorem, we deduce sufficient conditions that guarantee the uniform asymptotic stability and boundedness of solutions of a scalar real fourth-order delay differential equation. The Lyapunov function constructed for an ordinary fourth-order differential equation is seen to work for the delay system.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

scholarly journals Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
L. Padhy
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
T Tau

AbstractIn this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$\left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

scholarly journals Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22
Author(s):  
Zeqing Liu ◽  
Jingjing Zhu ◽  
Jeong Sheok Ume ◽  
Shin Min Kang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fourth Order ◽  
Delay Differential Equation ◽  
Approximate Solutions ◽  
Banach Fixed Point Theorem ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential

This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.

scholarly journals Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Youssef Raffoul ◽  
Habib Rai
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Infinite Delay ◽  
Zero Solution ◽  
Uniform Stability ◽  
Lyapunov Functionals ◽  
Integro Differential Equation ◽  
The Stability

AbstractIn [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation

scholarly journals Oscillation and nonoscillation of a delay differential equation

1994 ◽  
Vol 49 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Chunhai Kou ◽  
Weiping Yan ◽  
Jurang Yan
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
First Order ◽  
Oscillating Coefficients ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Oscillation And Nonoscillation

In this paper, some necessary and sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formare established. Several applications of our results improve and generalise some of the known results in the literature.

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