scholarly journals More Effective Conditions for Oscillatory Properties of Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 278 ◽  
Author(s):  
Taher A. Nofal ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Mihai Postolache
Keyword(s):  
Differential Equations ◽  
Middle Term ◽  
Riccati Substitution ◽  
Delay Differential ◽  
The Right ◽  
Nonlinear Delay Differential Equation ◽  
Effective Conditions ◽  
Oscillation Of Solutions ◽  
Nonlinear Delay ◽  
Comparison Technique

In this work, we present several oscillation criteria for higher-order nonlinear delay differential equation with middle term. Our approach is based on the use of Riccati substitution, the integral averaging technique and the comparison technique. The symmetry contributes to deciding the right way to study oscillation of solutions of this equations. Our results unify and improve some known results for differential equations with middle term. Some illustrative examples are provided.

scholarly journals Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 129 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Omar Bazighifan ◽  
Maria Alessandra Ragusa
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Riccati Substitution ◽  
Delay Differential ◽  
Oscillation Of Solutions ◽  
Comparison Technique

The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.

scholarly journals Oscillation Results for Nonlinear Higher-Order Differential Equations with Delay Term

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 446
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Youssef N. Raffoul
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Higher Order ◽  
Middle Term ◽  
Delay Term ◽  
Integral Averaging Technique ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Comparison Technique ◽  
Higher Order Differential Equations

The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.

scholarly journals Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Third Order ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Linear Differential ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

scholarly journals Asymptotic Properties of Solutions of Fourth-Order Delay Differential Equations

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 628 ◽  
Author(s):  
Clemente Cesarano ◽  
Sandra Pinelas ◽  
Faisal Al-Showaikh ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Asymptotic Properties ◽  
Riccati Transformation ◽  
Delay Differential ◽  
Oscillation Of Solutions ◽  
Comparison Technique

In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the oscillation of the certain second order differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. Some examples are also presented to test the strength and applicability of the results obtained.

scholarly journals Qualitative Behavior of Solutions of Second Order Differential Equations

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 777 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Qualitative Behavior ◽  
Second Order Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
Riccati Substitution ◽  
Delay Differential ◽  
The Right

In this work, we study the oscillation of second-order delay differential equations, by employing a refinement of the generalized Riccati substitution. We establish a new oscillation criterion. 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. We illustrate the results with some examples.

scholarly journals Oscillation of solutions to fourth-order delay differential equations with middle term

2019 ◽  
pp. 191-197 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
◽  
Ethiraju Thandapani ◽  
Osama Moaaz ◽  
Omar Bazighifan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Middle Term ◽  
Delay Differential ◽  
Oscillation Of Solutions

scholarly journals On the Oscillation of Solutions of Differential Equations with Neutral Term

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2709
Author(s):  
Fatemah Mofarreh ◽  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Mohammed A. Aiyashi ◽  
Alina-Daniela Vîlcu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Averaging Method ◽  
Oscillatory Behavior ◽  
Neutral Term ◽  
Even Order ◽  
Delay Differential ◽  
New Criteria ◽  
Oscillation Of Solutions ◽  
Comparison Technique

In this work, new criteria for the oscillatory behavior of even-order delay differential equations with neutral term are established by comparison technique, Riccati transformation and integral averaging method. The presented results essentially extend and simplify known conditions in the literature. To prove the validity of our results, we give some examples.

scholarly journals On the oscillation of nonlinear delay differential equations and their applications

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 788-796
Author(s):  
Omar Bazighifan ◽  
Sameh Askar
Keyword(s):  
Differential Equations ◽  
Medical Physics ◽  
Nonlinear Differential Equations ◽  
Mathematical Physics ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
W Prime ◽  
Equations With Delay ◽  
Nonlinear Delay ◽  
Comparison Technique

Abstract The oscillation of nonlinear differential equations is used in many applications of mathematical physics, biological and medical physics, engineering, aviation, complex networks, sociophysics and econophysics. The goal of this study is to create some new oscillation criteria for fourth-order differential equations with delay and advanced terms ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + ∑ j = 1 r β j ( x ) w k ( γ j ( x ) ) = 0 , {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+\mathop{\sum }\limits_{j=1}^{r}{\beta }_{j}(x){w}^{k}({\gamma }_{j}(x))=0, and ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + a 2 ( x ) h ( w ‴ ( x ) ) + β ( x ) f ( w ( γ ( x ) ) ) = 0 . {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+{a}_{2}(x)h({w}^{\prime\prime\prime }(x))+\beta (x)f(w(\gamma (x)))=0. The method is based on the use of the comparison technique and Riccati method to obtain these criteria. These conditions complement and extend some of the results published on this topic. Two examples are provided to prove the efficiency of the main results.

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