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 Oscillation for higher order differential equations with a middle term

2014 ◽  
Vol 2014 (1) ◽  
pp. 48 ◽  
Author(s):  
Miroslav Bartušek ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Middle Term ◽  
Higher Order Differential Equations

scholarly journals New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 454 ◽  
Author(s):  
Osama Moaaz ◽  
Shigeru Furuichi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Differential Inequalities ◽  
Neutral Differential Equations ◽  
First Order ◽  
A New Technique ◽  
Equations With Delay ◽  
Higher Order Differential Equations ◽  
First Order Differential Equations

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

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 Some Important Criteria for Oscillation of Non-Linear Differential Equations with Middle Term

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 346 ◽  
Author(s):  
Saad Althobati ◽  
Omar Bazighifan ◽  
Mehmet Yavuz
Keyword(s):  
Differential Equations ◽  
Comparison Method ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Middle Term ◽  
Oscillation Criteria ◽  
First Order ◽  
Non Linear ◽  
Linear Differential ◽  
Higher Order Differential Equations

In this work, we present new oscillation conditions for the oscillation of the higher-order differential equations with the middle term. We obtain some oscillation criteria by a comparison method with first-order equations. The obtained results extend and simplify known conditions in the literature. Furthermore, examining the validity of the proposed criteria is demonstrated via particular examples.

scholarly journals The boundary value problem of higher order differential equations with delay

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Zhimin He ◽  
Jianhua Shen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Equations With Delay ◽  
Higher Order Differential Equations

AbstractIn the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.

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.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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