scholarly journals Asymptotic properties of linear fourth order differential equations

1976 ◽  
Vol 59 (1) ◽  
pp. 45-45 ◽  
Author(s):  
Shair Ahmad
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Properties

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

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2015
Author(s):  
Omar Bazighifan ◽  
Maryam Al-Kandari ◽  
Khalil S. Al-Ghafri ◽  
F. Ghanim ◽  
Sameh Askar ◽  
...  
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Essential Role ◽  
Asymptotic Properties ◽  
Comparison Method ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Delay Differential

In this work, by using the comparison method and Riccati transformation, we obtain some oscillation criteria of solutions of delay differential equations of fourth-order in canonical form. These criteria complement those results in the literature. We give two examples to illustrate the main results. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

scholarly journals An Improved Criterion for the Oscillation of Fourth-Order Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 610 ◽  
Author(s):  
Omar Bazighifan ◽  
Marianna Ruggieri ◽  
Andrea Scapellato
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Variable Coefficients ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
Oscillation Of Solutions

The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients r ν w ‴ ν β ′ + ∑ i = 1 j q i ν y κ g i ν = 0 , where ν ≥ ν 0 and w ν : = y ν + p ν y σ ν . By using integral averaging technique, we get conditions to ensure oscillation of solutions of this equation. The obtained results improve and generalize the earlier ones; finally an example is given to illustrate the criteria.

scholarly journals Neutral Delay Differential Equations: Oscillation Conditions for the Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 101
Author(s):  
Omar Bazighifan ◽  
Hammad Alotaibi ◽  
Abd Allaah A. Mousa
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
Theoretical Support ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

The purpose of this article is to explore the asymptotic properties for a class of fourth-order neutral differential equations. Based on a comparison with the differential inequality of the first-order, we have provided new oscillation conditions for the solutions of fourth-order neutral differential equations. The obtained results can be used to develop and provide theoretical support for and to further develop the study of oscillation for a class of fourth-order neutral differential equations. Finally, we provide an illustrated example to demonstrate the effectiveness of our new criteria.

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 Important Criteria for Asymptotic Properties of Nonlinear Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1659
Author(s):  
Ahmed AlGhamdi ◽  
Omar Bazighifan ◽  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
The Subject ◽  
Oscillation Theorems ◽  
New Criteria

In this article, we prove some new oscillation theorems for fourth-order differential equations. New oscillation results are established that complement related contributions to the subject. We use the Riccati technique and the integral averaging technique to prove our results. As proof of the effectiveness of the new criteria, we offer more than one practical example.

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

scholarly journals Simplified and improved criteria for oscillation of delay differential equations of fourth order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. Moaaz ◽  
A. Muhib ◽  
D. Baleanu ◽  
W. Alharbi ◽  
E. E. Mahmoud
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Interesting Point ◽  
All Solutions ◽  
Special Cases ◽  
Delay Differential ◽  
Noncanonical Operator

AbstractAn interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples.

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