scholarly journals An Oscillation Criterion of Nonlinear Differential Equations with Advanced Term

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 843
Author(s):  
Omar Bazighifan ◽  
Alanoud Almutairi ◽  
Barakah Almarri ◽  
Marin Marin
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Nonlinear Differential Equations ◽  
Oscillation Criterion ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Specific Parameter ◽  
Parameter Values

The aim of the present paper is to provide oscillation conditions for fourth-order damped differential equations with advanced term. By using the Riccati technique, some new oscillation criteria, which ensure that every solution oscillates, are established. In fact, the obtained results extend, unify and correlate many of the existing results in the literature. Furthermore, two examples with specific parameter values are provided to confirm our results.

scholarly journals Improved Conditions for Oscillation of Functional Nonlinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 552 ◽  
Author(s):  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillation Criteria ◽  
Delay Differential ◽  
Oscillatory Properties

The aim of this work is to study oscillatory properties of a class of fourth-order delay differential equations. New oscillation criteria are obtained by using generalized Riccati transformations. This new theorem complements and improves a number of results reported in the literature. Some examples are provided to illustrate the main results.

scholarly journals Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 590 ◽  
Author(s):  
Omar Bazighifan ◽  
Ioannis Dassios
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Riccati Technique ◽  
Oscillation Criteria

In this paper, we deal with the oscillation of fourth-order nonlinear advanced differential equations of the form r t y ‴ t α ′ + p t f y ‴ t + q t g y σ t = 0 . We provide oscillation criteria for this type of equations, and examples to illustrate the criteria.

scholarly journals New Oscillation Criteria for Neutral Delay Differential Equations of Fourth-Order

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1277
Author(s):  
Saeed Althubiti ◽  
Omar Bazighifan ◽  
Hammad Alotaibi ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Riccati Technique ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

New oscillatory properties for the oscillation of solutions to a class of fourth-order delay differential equations with several deviating arguments are established, which extend and generalize related results in previous studies. Some oscillation results are established by using the Riccati technique under the case of canonical coefficients. The symmetry plays an important and fundamental role in the study of the oscillation of solutions of the equations. Examples are given to prove the significance of the new theorems.

scholarly journals Oscillation Conditions for Certain Fourth-Order Non-Linear Neutral Differential Equation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1096 ◽  
Author(s):  
Ioannis Dassios ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Neutral Differential Equation ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Non Linear ◽  
The Right ◽  
Oscillation Of Solutions

In this work, new conditions were obtained for the oscillation of solutions of fourth-order non-linear neutral differential equations (NDEs) using the Riccati technique. These oscillation criteria complement and improve those of Chatzarakis et al. (2019). Symmetry plays an important role in determining the right way to study these equation. An example is given to illustrate our theory.

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.

Oscillation Criteria for Second-Order Nonlinear Differential Equations with Damping Term

2003 ◽  
Vol 10 (4) ◽  
pp. 771-784
Author(s):  
Qi-Ru Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Damping Term ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Technique

Abstract By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrate the importance of our results are included.

scholarly journals Comparison theorems for fourth order differential equations

1986 ◽  
Vol 9 (1) ◽  
pp. 105-109
Author(s):  
Garret J. Etgen ◽  
Willie E. Taylor
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Linear Equations ◽  
Oscillation Criterion ◽  
Comparison Theorems ◽  
Positive Continuous Function ◽  
Order Linear ◽  
All Solutions

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equationsyiv−p(x)y=0andyiv+p(x)y=0, wherepis a positive, continuous function defined on[0,∞). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.

scholarly journals Oscillatory behavior of nonlinear differential equations with deviating arguments

1985 ◽  
Vol 31 (1) ◽  
pp. 127-136 ◽  
Author(s):  
S.R. Grace ◽  
B.S. Lalli
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Image Position

New oscillation criteria for nonlinear differential equations with deviating arguments of the formn even, are established.

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