scholarly journals Oscillation and Asymptotic Behaviour of a Higher-Order Nonlinear Neutral-Type Functional Differential Equation with Oscillating Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Mustafa Kemal Yildiz ◽  
Emrah Karaman ◽  
Hülya Durur
Keyword(s):  
Neutral Type ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Bounded Solutions ◽  
Neutral Delay ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Oscillating Coefficients ◽  
Functional Differential ◽  
Delay Differential

We will study oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type:[y(t)+p(t)f(y(τ(t)))](n)+q(t)h(y(σ(t)))=0,t≥t0,t∈R, wherep∈C([t0,∞),R),limt→∞p(t)=0,q∈C([t0,∞),R+),τ(t),σ(t)∈C([t0,∞),R),τ(t),σ(t)<t,lim⁡t→∞τ(t),σ(t)=∞, andf,h∈C(R,R). We obtain sufficient conditions for the oscillation of all solutions of this equation.

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.

Unbounded oscillation of fourth order functional differential equations

2020 ◽  
Vol 70 (5) ◽  
pp. 1153-1164
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Unbounded Solutions ◽  
Neutral Delay Differential Equations ◽  
Functional Differential ◽  
Delay Differential ◽  
T Tau

AbstractIn this paper, sufficient conditions for oscillation of unbounded solutions of a class of fourth order neutral delay differential equations of the form$$\begin{array}{} \displaystyle (r(t)(y(t)+p(t)y(t-\tau))'')''+q(t)G(y(t-\alpha))-h(t)H(y(t-\sigma))=0 \end{array}$$are discussed under the assumption$$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}\text{d}~~ t=\infty \end{array}$$

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 Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ruba Al-Hamouri ◽  
Ali Zein
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Even Order ◽  
Delay Differential ◽  
Oscillation Of Solutions

We establish sufficient conditions for the oscillation of solutions of even order neutral type differential equations of the form[r(t)[x(t)+p(t)x(τ(t))](n−1)]′+q(t)f(x(σ(t)))=0.

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 New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing 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.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

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.

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