scholarly journals Oscillation of Third-Order Neutral Delay Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Tongxing Li ◽  
Chenghui Zhang ◽  
Guojing Xing
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
The Third ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

The purpose of this paper is to examine oscillatory properties of the third-order neutral delay differential equation[a(t)(b(t)(x(t)+p(t)x(σ(t)))′)′]′+q(t)x(τ(t))=0. Some oscillatory and asymptotic criteria are presented. These criteria improve and complement those results in the literature. Moreover, some examples are given to illustrate the main results.

Oscillations of Neutral Delay Differential Equations

1986 ◽  
Vol 29 (4) ◽  
pp. 438-445 ◽  
Author(s):  
G. Ladas ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

AbstractThe oscillatory behavior of the solutions of the neutral delay differential equationwhere p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

scholarly journals Oscillation results for second order half-linear neutral delay differential equations with "maxima"

2017 ◽  
Vol 48 (3) ◽  
pp. 289-299 ◽  
Author(s):  
Selvarangam Srinivasan ◽  
Rani Bose ◽  
Ethiraju Thandapani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, we present some oscillation criteria for the second order half-linear neutral delay differential equation with ``maxima" of the from\begin{equation*}\left(r(t)((x(t)+p(t)x(\tau(t)))')^{\alpha}\right)'+q(t) \max_{[\sigma(t),\;t]}x^{\alpha}(s)=0\end{equation*}under the condition $\int_{t_0}^{\infty}\frac{1}{r^{1/ \alpha}(t)}dt<\infty.$ The results obtained here extend and complement to some known results in the literature. Examples are provided in support of our results.

scholarly journals On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Youliang Fu ◽  
Yazhou Tian ◽  
Cuimei Jiang ◽  
Tongxing Li
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Third Order ◽  
Deviating Arguments ◽  
Neutral Delay Differential Equation ◽  
Distributed Deviating Arguments ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

scholarly journals Asymptotic properties of trinomial delay differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 71-79
Author(s):  
Jozef Džurina ◽  
Renáta Kotorová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Canonical Form ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
The Third ◽  
Delay Differential ◽  
New Criteria

AbstractNew criteria for asymptotic properties of the solutions of the third order delay differential equation, by transforming this equation to its binomial canonical form are presented

scholarly journals Oscillation Criteria for a Class of Third-Order Damped Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1988
Author(s):  
Elmetwally M. Elabbasy ◽  
Belgees Qaraad ◽  
Thabet Abdeljawad ◽  
Osama Moaaz
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Equation ◽  
Neutral Delay ◽  
Third Order ◽  
Middle Term ◽  
Neutral Differential Equations ◽  
The Third ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, we study the asymptotic and oscillatory properties of a certain class of third-order neutral delay differential equations with middle term. We obtain new characterizations of oscillation of the third-order neutral equation in terms of oscillation of a related, well-studied, second-order linear equation without damping. An Example is provided to illustrate the main results.

scholarly journals Nonoscillatory solutions of neutral delay differential equations

1993 ◽  
Vol 48 (3) ◽  
pp. 475-483 ◽  
Author(s):  
Ming-Po Chen ◽  
J.S. Yu ◽  
Z.C. Wang
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Nonoscillatory Solution ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Image Position ◽  
Delay Differential

Consider the following neutral delay differential equationwhere p ∈ R, τ ∈ (0, ∞), δ ∈ R+ = (0, ∞) and Q ∈ (C([t0, ∞), R). We show that ifthen Equation (*)has a nonoscillatory solution when p ≠ –1. We also deal in detail with a conjecture of Chuanxi, Kulenovic and Ladas, and Györi and Ladas.

scholarly journals On the oscillation of third-order quasi-linear delay differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Tongxing Li ◽  
Chenghui Zhang ◽  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
The Third ◽  
Linear Delay ◽  
Delay Differential

Abstract The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation , (E) where and τ(t) ≤ t. We establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.

scholarly journals Oscillation Results for Third-Order Semi-Canonical Quasi-Linear Delay Differential Equations

2021 ◽  
Vol 8 (1) ◽  
pp. 228-238
Author(s):  
K. Saranya ◽  
V. Piramanantham ◽  
E. Thandapani
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Main Idea ◽  
Third Order ◽  
The Third ◽  
Linear Delay ◽  
Delay Differential

Abstract The main purpose of this paper is to study the oscillatory properties of solutions of the third-order quasi-linear delay differential equation ℒ y ( t ) + f ( t ) y β ( σ ( t ) ) = 0 {\cal L}y(t) + f(t){y^\beta }(\sigma (t)) = 0 where ℒy(t) = (b(t)(a(t)(y 0(t)) )0)0 is a semi-canonical differential operator. The main idea is to transform the semi-canonical operator into canonical form and then obtain new oscillation results for the studied equation. Examples are provided to illustrate the importance of the main results.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

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