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 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 Fourth-Order Differential Equation with Deviating Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
M. Bartušek ◽  
M. Cecchi ◽  
Z. Došlá ◽  
M. Marini
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Order Equation ◽  
Asymptotically Linear ◽  
Middle Term ◽  
Deviating Argument ◽  
Necessary And Sufficient ◽  
Fourth Order Differential Equation

We consider the fourth-order differential equation with middle-term and deviating argumentx(4)(t)+q(t)x(2)(t)+r(t)f(x(φ(t)))=0, in case when the corresponding second-order equationh″+q(t)h=0is oscillatory. Necessary and sufficient conditions for the existence of bounded and unbounded asymptotically linear solutions are given. The roles of the deviating argument and the nonlinearity are explained, too.

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 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.

scholarly journals New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2388
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Ali Muhib ◽  
Sayed K. Elagan ◽  
Mohammed Zakarya
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Delay Differential Equation ◽  
Oscillation Criterion ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Riccati Substitution ◽  
Delay Differential ◽  
New Criterion

In this study, a new oscillation criterion for the fourth-order neutral delay differential equation ruxu+puxδu‴α′+quxβϕu=0,u≥u0 is established. By introducing a Riccati substitution, we obtain a new criterion for oscillation without requiring the existence of the unknown function. Furthermore, the new criterion improves and complements the previous results in the literature. The results obtained are illustrated by an example.

scholarly journals Oscillation of the even - order delay linear differential equation

2015 ◽  
Vol 31 (1) ◽  
pp. 69-76
Author(s):  
J. DZURINA ◽  
◽  
B. BACULIKOVA ◽  
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Necessary And Sufficient Conditions ◽  
Even Order ◽  
Linear Differential ◽  
Delay Differential ◽  
Necessary And Sufficient

In the paper we offer criteria for oscillation of the even order delay differential equation y(n)(t) + p(t)y(ct) = 0 We provide detail analysis of the properties of this equation, we offer necessary and sufficient conditions for oscillation of studied equation and we fulfill the gap in the oscillation theory.

scholarly journals Oscillation of Nonlinear Differential Equations with Advanced Arguments

2008 ◽  
Vol 5 (4) ◽  
pp. 652-659
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Oscillatory Solutions ◽  
All Solutions ◽  
Delay Differential ◽  
Necessary And Sufficient

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.

scholarly journals Necessary and Sufficient Conditions for Oscillation of Second-Order Delay Differential Equations

2020 ◽  
Vol 75 (1) ◽  
pp. 135-146
Author(s):  
Shyam Sundar Santra
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractIn this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form {\left( {r{{\left( {x'} \right)}^\gamma }} \right)^\prime }\left( t \right) + q\left( t \right){x^\alpha }\left( {\tau \left( t \right)} \right) = 0Under the assumption ∫∞(r(n))−1/γdη=∞, we consider the two cases when γ > α and γ < α. Further, some illustrative examples showing applicability of the new results are included, and state an open problem.

scholarly journals Oscillation Theorems for Nonlinear Differential Equations of Fourth-Order

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 520 ◽  
Author(s):  
Osama Moaaz ◽  
Ioannis Dassios ◽  
Omar Bazighifan ◽  
Ali Muhib
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Middle Term ◽  
Oscillation Theorems ◽  
Fourth Order Differential Equation

We study the oscillatory behavior of a class of fourth-order differential equations and establish sufficient conditions for oscillation of a fourth-order differential equation with middle term. Our theorems extend and complement a number of related results reported in the literature. One example is provided to illustrate the main results.

scholarly journals Stability Properties of a Discretized Neutral Delay Differential Equation

2013 ◽  
Vol 54 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Jana Hrabalová
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Delay Differential Equation ◽  
Stability Region ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Asymptotic Stability Region ◽  
Delay Differential ◽  
Necessary And Sufficient

Abstract The paper discusses the asymptotic stability region of a discretization of a linear neutral delay differential equation x′(t) = ax(t - τ) + bx'(t - τ). We present necessary and sufficient conditions specifying this region and describe some of its properties.

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