scholarly journals New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 325 ◽  
Author(s):  
K. S. Vidhyaa ◽  
John R. Graef ◽  
E. Thandapani
Keyword(s):  
Differential Equations ◽  
Additional Result ◽  
Oscillation Theorem ◽  
Third Order ◽  
Transformation Technique ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation. The main result in this paper is an oscillation theorem obtained by comparing the equation under investigation to two first order linear delay differential equations. An additional result is obtained by using a Riccati transformation technique. Examples are provided to show the importance of the main results.

scholarly journals Oscillation of Nonlinear First Order Neutral Differential Equations

2007 ◽  
Vol 4 (3) ◽  
pp. 485-490
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Integral Conditions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

scholarly journals Oscillations of First Order Linear Delay Differential Equations with positive and negative coefficients

2011 ◽  
Vol 8 (3) ◽  
pp. 806-809
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.

Oscillation in Differential Equations with Positive and Negative Coefficients

1990 ◽  
Vol 33 (4) ◽  
pp. 442-451 ◽  
Author(s):  
G. Ladas ◽  
C. Qian
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Image Position ◽  
Delay Differential

AbstractWe obtain sufficient conditions for the oscillation of all solutions of the linear delay differential equation with positive and negative coefficientswhereExtensions to neutral differential equations and some applications to the global asymptotic stability of the trivial solution are also given.

scholarly journals COMPARISON THEOREMS ON THE OSCILLATION AND ASYMPTOTIC BEHAVIOUR OF HIGHER-ORDER NEUTRAL DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 52 (1) ◽  
pp. 107-114 ◽  
Author(s):  
BAŞAK KARPUZ ◽  
ÖZKAN ÖCALAN ◽  
SERMIN ÖZTÜRK
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Delay Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Delay Differential ◽  
Asymptotic Behaviours

AbstractIn this work, oscillatory and asymptotic behaviours of all solutions of higher-order neutral differential equations are compared with first-order delay differential equations, depending on two different ranges of the coefficient associated with the neutral part. Some simple examples are given to compare our results with the existing results in the literature and to illustrate the significance and applicability of our new results. Our results generalise, improve and correct some of the existing results in the literature.

scholarly journals Third-order neutral differential equations of the mixed type: Oscillatory and asymptotic behavior

2021 ◽  
Vol 19 (2) ◽  
pp. 1649-1658
Author(s):  
B. Qaraad ◽  
◽  
O. Moaaz ◽  
D. Baleanu ◽  
S. S. Santra ◽  
...  
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Differential Inequalities ◽  
Riccati Transformation ◽  
Third Order ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
New Criteria ◽  
Comparison Technique

<abstract><p>In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results.</p></abstract>

scholarly journals New Results for Kneser Solutions of Third-Order Nonlinear Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 686 ◽  
Author(s):  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Nonlinear Equation ◽  
Delay Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria ◽  
Nonlinear Delay

In this paper, we consider a certain class of third-order nonlinear delay differential equations r w ″ α ′ v + q v x β ς v = 0 , for v ≥ v 0 , where w v = x v + p v x ϑ v . We obtain new criteria for oscillation of all solutions of this nonlinear equation. Our results complement and improve some previous results in the literature. An example is considered to illustrate our main results.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

scholarly journals First Order Nonlinear Neutral Delay Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 347-349 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

scholarly journals On the oscillation of the solutions to delay and difference equations

2009 ◽  
Vol 43 (1) ◽  
pp. 173-187
Author(s):  
Khadija Niri ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Discrete Analogue ◽  
Optimal Conditions ◽  
Nondecreasing Sequence ◽  
Real Numbers ◽  
First Order ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

Abstract Consider the first-order linear delay differential equation xʹ(t) + p(t)x(τ(t)) = 0, t≥ t<sub>0</sub>, (1) where p, τ ∈ C ([t<sub>0</sub>,∞, ℝ<sup>+</sup>, τ(t) is nondecreasing, τ(t) < t for t ≥ t<sup>0</sup> and lim<sub>t→∞</sub> τ(t) = ∞, and the (discrete analogue) difference equation Δx(n) + p(n)x(τ(n)) = 0, n= 0, 1, 2,…, (1)ʹ where Δx(n) = x(n + 1) − x(n), p(n) is a sequence of nonnegative real numbers and τ(n) is a nondecreasing sequence of integers such that τ(n) ≤ n − 1 for all n ≥ 0 and lim<sub>n→∞</sub> τ(n) = ∞. Optimal conditions for the oscillation of all solutions to the above equations are presented.

Sign in / Sign up

Export Citation Format

Share Document