scholarly journals Establishing New Criteria for Oscillation of Odd-Order Nonlinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 937
Author(s):  
Osama Moaaz ◽  
Jan Awrejcewicz ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Odd Order ◽  
All Solutions ◽  
New Criteria

By establishing new conditions for the non-existence of so-called Kneser solutions, we can generate sufficient conditions to ensure that all solutions of odd-order equations are oscillatory. Our results improve and expand the previous results in the literature.

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

scholarly journals Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments

2020 ◽  
Vol 10 (17) ◽  
pp. 5952
Author(s):  
Ali Muhib ◽  
Thabet Abdeljawad ◽  
Osama Moaaz ◽  
Elmetwally M. Elabbasy
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Comparison Theorems ◽  
Iterative Technique ◽  
Deviating Arguments ◽  
First Order ◽  
Odd Order ◽  
All Solutions ◽  
Delay Differential ◽  
New Criteria

Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimates for positive solutions of the studied equation, using an iterative technique. Moreover, the iterative technique allows us to test the oscillation, even when the related results fail to apply. By establishing new comparison theorems that compare the nth-order equations with one or a couple of first-order delay differential equations, we obtain new conditions for oscillation of all solutions of the studied equation. To show the importance of our results, we provide two examples.

scholarly journals New Aspects for Non-Existence of Kneser Solutions of Neutral Differential Equations with Odd-Order

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 494 ◽  
Author(s):  
Osama Moaaz ◽  
Dumitru Baleanu ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
All Solutions

Some new oscillatory and asymptotic properties of solutions of neutral differential equations with odd-order are established. Through the new results, we give sufficient conditions for the oscillation of all solutions of the studied equations, and this is an improvement of the relevant results. The efficiency of the obtained criteria is illustrated via example.

scholarly journals Oscillation of Nonlinear Differential Equations with Advanced Arguments

2008 ◽  
Vol 5 (4) ◽  
pp. 652-659
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Oscillatory Solutions ◽  
All Solutions ◽  
Delay Differential ◽  
Necessary And Sufficient

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.

scholarly journals Oscillation Criteria for Third-Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
George E. Chatzarakis ◽  
Said R. Grace ◽  
Irena Jadlovská ◽  
Tongxing Li ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
New Criteria

New sufficient conditions for the oscillation of all solutions to a class of third-order Emden–Fowler differential equations with unbounded neutral coefficients are established. The criteria obtained essentially improve related results in the literature. In particular, as opposed to known results, new criteria can distinguish solutions of third-order differential equations with different behaviors. Examples are also provided to illustrate the 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.

scholarly journals Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

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 Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

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