On the Oscillatory Properties of Solutions of Second-Order Damped Delay Differential Equations

In the work, a new oscillation condition was created for second-order damped delay differential equations with a non-canonical operator. The new criterion is of an iterative nature which helps to apply it even when the previous relevant results fail to apply. An example is presented in order to illustrate the significance of the results.

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New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

Mathematics ◽

10.3390/math9101111 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1111

Author(s):

Shyam Sundar Santra ◽

Abhay Kumar Sethi ◽

Osama Moaaz ◽

Khaled Mohamed Khedher ◽

Shao-Wen Yao

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Second Order ◽

Riccati Transformation ◽

Neutral Delay ◽

Canonical Operator ◽

Second Order Differential Equations ◽

Neutral Delay Differential Equations ◽

Delay Differential ◽

Oscillation Theorems

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

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Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽

10.3390/sym13020318 ◽

2021 ◽

Vol 13 (2) ◽

pp. 318

Author(s):

Osama Moaaz ◽

Amany Nabih ◽

Hammad Alotaibi ◽

Y. S. Hamed

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Mixed Type ◽

Relevant Literature ◽

Sufficient Conditions ◽

Oscillatory Behavior ◽

Second Order ◽

Neutral Differential Equations ◽

Delay Differential ◽

Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

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The use of polynomial spline functions for the solution of system of second order delay differential equations

International Journal of Computer Mathematics ◽

10.1080/00207160701769617 ◽

2009 ◽

Vol 86 (7) ◽

pp. 1167-1181 ◽

Cited By ~ 3

Author(s):

Mohamed A. Ramadan ◽

Abd- El -Aziz El-Sherbeiny ◽

Mahmoud N. Sherif

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Polynomial Spline ◽

Second Order ◽

Spline Functions ◽

Delay Differential

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

Advances in Difference Equations ◽

10.1186/s13662-021-03299-8 ◽

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.

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New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Mathematics ◽

10.3390/math9111159 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1159

Author(s):

Shyam Sundar Santra ◽

Omar Bazighifan ◽

Mihai Postolache

Keyword(s):

Fluid Dynamics ◽

Neural Networks ◽

Differential Equations ◽

Delay Differential Equations ◽

Sufficient Conditions ◽

Second Order ◽

Qualitative Behavior ◽

Neutral Differential Equations ◽

Second Order Differential Equations ◽

Delay Differential

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

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Global solutions of a singular initial value problem to second order nonlinear delay differential equations

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2005.12.005 ◽

2006 ◽

Vol 43 (7-8) ◽

pp. 854-869 ◽

Cited By ~ 8

Author(s):

R.P. Agarwal ◽

Ch.G. Philos ◽

P.Ch. Tsamatos

Keyword(s):

Differential Equations ◽

Initial Value Problem ◽

Delay Differential Equations ◽

Global Solutions ◽

Second Order ◽

Initial Value ◽

Singular Initial Value Problem ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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Oscillatory and non-oscillatory behaviour of second-order neutral delay differential equations

Applied Mathematics and Computation ◽

10.1016/s0096-3003(01)00335-6 ◽

2003 ◽

Vol 135 (2-3) ◽

pp. 333-344 ◽

Cited By ~ 5

Author(s):

Sabah Hafez Abdallah

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Second Order ◽

Oscillatory Behaviour ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Delay Differential

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Second-Order Delay Differential Equations to Deal the Experimentation of Internet of Industrial Things via Haar Wavelet Approach

Wireless Communications and Mobile Computing ◽

10.1155/2021/5551497 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Yongtao Xuan ◽

Rohul Amin ◽

Fakhar Zaman ◽

Zohaib Khan ◽

Imad Ullah ◽

...

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Numerical Approach ◽

Haar Wavelet ◽

Second Order ◽

Algebraic Equations ◽

Elimination Algorithm ◽

Collocation Points ◽

Delay Differential ◽

Mean Square Errors

In this article, an efficient numerical approach for the solution of second-order delay differential equations to deal with the experimentation of the Internet of Industrial Things (IIoT) is presented. With the help of the Haar wavelet technique, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for various collocation points. The results show that the Haar wavelet method is an effective method for solving delay differential equations of second order. The convergence rate is also measured for various collocation points, which is almost equal to 2.

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Oscillation Criteria for Second Order Neutral Differential Equations

Canadian Journal of Mathematics ◽

10.4153/cjm-1996-044-6 ◽

1996 ◽

Vol 48 (4) ◽

pp. 871-886 ◽

Cited By ~ 14

Author(s):

Horng-Jaan Li ◽

Wei-Ling Liu

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Delay Differential Equations ◽

Second Order ◽

Neutral Delay ◽

Oscillation Criteria ◽

Neutral Differential Equations ◽

Neutral Delay Differential Equation ◽

Image Position ◽

Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

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