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 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 The Oscillation of a Class of the Fractional-Order Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qianli Lu ◽  
Feng Cen
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Analysis Method ◽  
Constant Coefficients ◽  
Delay Differential ◽  
Necessary And Sufficient

Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this,α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.

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 for oscillation of first order neutral delay difference equations

2015 ◽  
Vol 3 (2) ◽  
pp. 61
Author(s):  
A. Murgesan ◽  
P. Sowmiya
Keyword(s):  
Difference Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
First Order ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference

<p>In this paper, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the first order neutral delay difference equation with constant coefficients of the form <br />\begin{equation*} \quad \quad \quad \quad \Delta[x(n)-px(n-\tau)]+qx(n-\sigma)=0, \quad \quad n\geq n_0 \quad \quad \quad \quad \quad \quad {(*)} \end{equation*}<br />by constructing several suitable auxiliary functions. Some examples are also given to illustrate our results.</p>

scholarly journals Conditions for oscillation of first order neutral delay differential equations

1997 ◽  
Vol 56 (1) ◽  
pp. 1-16
Author(s):  
Ziwen Jiang
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, some new sufficient conditions for oscillation of first order neutral delay differential equations with several variable coefficients are obtained. These sufficient conditions include and are in many cases weaker than those known.

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 Asymptotic behavior of solutions of nonlinear neutral delay differential equations

2014 ◽  
Vol 45 (1) ◽  
pp. 21-30
Author(s):  
Gengping Wei
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
T Tau

This paper is concerned with the nonlinear neutral delay differential equation with positive and negative coefficients $$ [x(t)-c(t)x(t-\tau)]'+p(t)f(x(t-\delta))-q(t)f(x(t-\sigma))=0,\,\ t\geq t_0, $$ where $\tau\in(0,\infty)$, $\delta$ and $\sigma \in[0,\infty)$, $c(t)\in C([t_0,\infty), R)$, $p(t$) and $q(t)\in C([t_0,\infty), [0,\infty))$, $f\in C(R,R)$. Sufficient conditions are obtained under which every solution of the above equation is bounded and tends to a constant as $t\to\infty$. Our results extend and improve some known results.

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 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.

Sign in / Sign up

Export Citation Format

Share Document