scholarly journals Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 371 ◽  
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
The Right

In this paper, new sufficient conditions for oscillation of fourth-order neutral differential equations are established. One objective of our paper is to further improve and complement some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.

scholarly journals A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 379 ◽  
Author(s):  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Averaging Method ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
The Right ◽  
Type Oscillation ◽  
Oscillation Of Solutions

Some sufficient conditions are established for the oscillation of fourth order neutral differential equations of the form r t z ‴ t α ′ + q t x β σ t = 0 , where z t : = x t + p t x τ t . By using the technique of Riccati transformation and integral averaging method, we get conditions to ensure oscillation of solutions of this equation. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. Moreover, the importance of the obtained conditions is illustrated via some examples.

scholarly journals Behavior of Non-Oscillatory Solutions of Fourth-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 477 ◽  
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Riccati Transformation ◽  
Oscillatory Solutions ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Generalized Riccati Transformation ◽  
Correct Direction ◽  
The Right

In this paper, we deal with the asymptotics and oscillation of the solutions of fourth-order neutral differential equations of the form r t z ‴ t α ′ + q t x α g t = 0 , where z t : = x t + p t x δ t . By using a generalized Riccati transformation, we study asymptotic behavior and derive some new oscillation criteria. Our results extend and improve some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.

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.

Oscillations of Second Order Neutral Differential Equations

1993 ◽  
Vol 36 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Shigui Ruan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractIn this paper, we consider the oscillatory behavior of the second order neutral delay differential equationwhere t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

scholarly journals Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

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 On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 134 ◽  
Author(s):  
Shyam Sundar Santra ◽  
Ioannis Dassios ◽  
Tanusri Ghosh
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Second Order ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Non Linear ◽  
Delay Differential

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

scholarly journals Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1248 ◽  
Author(s):  
Omar Bazighifan ◽  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Delay Argument ◽  
The Right ◽  
Equations With Delay ◽  
Oscillatory Properties

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.

scholarly journals Some new oscillation criteria of fourth-order quasi-linear differential equations with neutral term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Saeed Althubiti ◽  
Fahad Alsharari ◽  
Omar Bazighifan ◽  
George E. Chatzarakis
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Average Technique ◽  
Neutral Differential Equations ◽  
Linear Differential ◽  
Fourth Order Equations ◽  
Delay Differential ◽  
Integral Average

AbstractIn this article, we are interested in studying the asymptotic behavior of fourth-order neutral differential equations. Despite the growing interest in studying the oscillatory behavior of delay differential equations of second-order, fourth-order equations have received less attention. We get more than one criterion to check the oscillation by the generalized Riccati method and the integral average technique. Our results are an extension and complement to some results published in the literature. Examples are given to prove the significance of new theorems.

scholarly journals Oscillatory behavior of solutions of certain third order mixed neutral differential equations

2013 ◽  
Vol 44 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Ethiraj Thandapani ◽  
Renu Rama
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Positive Integers

The objective of this paper is to study the oscillatory and asymptotic properties of third order mixed neutral differential equation of the form $$ (a(t) [x(t) + b(t) x(t - \tau_{1}) + c(t) x(t + \tau_{2})]'')' + q(t) x^{\alpha}(t - \sigma_{1}) + p(t) x^{\beta}(t + \sigma_{2}) = 0 $$where $a(t), b(t), c(t), q(t)$ and $p(t)$ are positive continuous functions, $\alpha$ and $\beta$ are ratios of odd positive integers, $\tau_{1}, \tau_{2}, \sigma_{1}$ and $\sigma_{2}$ are positive constants. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converge to zero. Some examples are provided to illustrate the main results.

Sign in / Sign up

Export Citation Format

Share Document