scholarly journals Stability and Square Integrability of Solutions to third order Neutral Delay Differential Equations

2018 ◽  
Vol 71 (1) ◽  
pp. 81-97 ◽  
Author(s):  
John R. Graef ◽  
Linda D. Oudjedi ◽  
Moussadek Remili
Keyword(s):  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Square Integrability ◽  
Delay Differential

Abstract In this paper, sufficient conditions to guarantee the square integrability of all solutions and the asymptotic stability of the zero solution of a non-autonomous third-order neutral delay differential equation are established. An example is given to illustrate the main results.

scholarly journals On the oscillation of first-order neutral delay differential equations with real coefficients

2002 ◽  
Vol 29 (4) ◽  
pp. 245-249 ◽  
Author(s):  
Ibrahim R. Al-Amri
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
T Tau

We prove sufficient conditions for the oscillation of all solutions of a scalar first-order neutral delay differential equationx˙(t)−cx˙(t−τ)+∑i=1npix(t−σi)=0for all0<c<1,τ,σi>0, andpi∈ℝ,i=1,2,…,n.

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 Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. Some examples are inserted to illustrate our results.

scholarly journals Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Songbai Guo ◽  
Youjian Shen ◽  
Binbin Shi
Keyword(s):  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Constant Coefficients ◽  
Delay Differential ◽  
Necessary And Sufficient

We are concerned with oscillation of the first order neutral delay differential equation[x(t)−px(t−τ)]′+qx(t−σ)=0with constant coefficients, and we obtain some necessary and sufficient conditions of oscillation for all the solutions in respective cases0<p<1andp>1.

scholarly journals Oscillation of neutral delay differential equations

1992 ◽  
Vol 45 (2) ◽  
pp. 195-200 ◽  
Author(s):  
Jianshe Yu ◽  
Zhicheng Wang ◽  
Chuanxi Qian
Keyword(s):  
Delay Differential Equations ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Open Problems ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Image Position ◽  
Delay Differential

Consider the following neutral delay differential equationwhere P ∈ ℝ, T ∈ (0, ∞), σ ∈ (0, ∞) and Q ∈ C[(t0, ∞), [0, ∞)]. We obtain a sufficient condition for the oscillation of all solutions of Equation (*) with P = −1, which does not require thatBut, for the cases −1 < P < 0 and P < −1, we show that (**) is a necessary condition for the oscillation of all solutions of Equation (*). These new results solve some open problems in the literature.

scholarly journals Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1177 ◽  
Author(s):  
George E. Chatzarakis ◽  
Jozef Džurina ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Differential Inequalities ◽  
Neutral Delay ◽  
Third Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.

Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
P. Mishra
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
T Tau

AbstractIn this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation $$ (r(t)(y(t) - p(t)y(t - \tau ))')' + q(t)G(y(h(t)) = f(t) $$ has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C (2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.

scholarly journals ASYMPTOTIC STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION

2002 ◽  
Vol 45 (2) ◽  
pp. 333-347 ◽  
Author(s):  
X. H. Tang ◽  
Xingfu Zou
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Primary 34K20 ◽  
All Solutions ◽  
Delay Differential ◽  
T Tau

AbstractThe uniform stability of the zero solution and the asymptotic behaviour of all solutions of the neutral delay differential equation$$ [x(t)-P(t)x(t-\tau)]'+Q(t)x(t-\sigma)=0,\quad t\ge t_0, $$are investigated, where $\tau,\sigma\in(0,\infty)$, $P\in C([t_0,\infty),\mathbb{R})$, and $Q\in C([t_0,\infty), [0,\infty))$. The obtained sufficient conditions improve the existing results in the literature.AMS 2000 Mathematics subject classification: Primary 34K20; 34K15; 34K40

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.

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