scholarly journals Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main results.

scholarly journals Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 412 ◽  
Author(s):  
Osama Moaaz ◽  
Ioannis Dassios ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Type Criterion ◽  
Even Order

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using the technique of Riccati transformation and comparison principles with the second-order differential equations, we obtain a new Philos-type criterion. Our results extend and improve some known results in the literature. An example is given to illustrate our main results.

scholarly journals Oscillatory Criteria for Higher Order Functional Differential Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Peiguang Wang ◽  
Hai Cai
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

We investigate a class of higher order functional differential equations with damping. By using a generalized Riccati transformation and integral averaging technique, some oscillation criteria for the differential equations are established.

scholarly journals Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

scholarly journals Improved criteria for oscillation of noncanonical neutral differential equations of even order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Osama Moaaz ◽  
Higinio Ramos ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Equations ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Even Order ◽  
New Criteria

AbstractIn this work, we aim at studying the asymptotic and oscillatory behavior of even-order neutral delay noncanonical differential equations. To the best of our knowledge, most of the related previous works are concerned only with neutral equations in the canonical case. Our new oscillation criteria essentially improve, simplify, and complement related results in the literature, especially those from a paper by Li and Rogovchenko (Abstr. Appl. Anal. 2014:395368, 2014). Some examples are presented that illustrate the importance of the new criteria.

scholarly journals Emden–Fowler-type neutral differential equations: oscillatory properties of solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Bazighifan ◽  
Alanoud Almutairi
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Comparison Method ◽  
Riccati Transformation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Delay Differential ◽  
Oscillatory Properties

AbstractIn this paper, we study the oscillation of a class of fourth-order Emden–Fowler delay differential equations with neutral term. Using the Riccati transformation and comparison method, we establish several new oscillation conditions. These new conditions complement a number of results in the literature. We give examples to illustrate our main results.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

scholarly journals Multiple Techniques for Studying Asymptotic Properties of a Class of Differential Equations with Variable Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1112
Author(s):  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Method ◽  
Variable Coefficients ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
Oscillatory Properties

This manuscript is concerned with the oscillatory properties of 4th-order differential equations with variable coefficients. The main aim of this paper is the combination of the following three techniques used: the comparison method, Riccati technique and integral averaging technique. Two examples are given for applying the criteria.

scholarly journals Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 656 ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Properties

This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will establish some new oscillation criteria for this equation. Some examples are considered to illustrate the main results.

scholarly journals Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

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