scholarly journals Existence of oscillatory solutions of forced second order delay differential equations

2011 ◽  
Vol 24 (8) ◽  
pp. 1455-1460 ◽  
Author(s):  
Jurang Yan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Delay Differential

scholarly journals ON THE BEHAVIOUR OF THE OSCILLATORY SOLUTIONS OF SECOND-ORDER LINEAR UNSTABLE TYPE DELAY DIFFERENTIAL EQUATIONS

2005 ◽  
Vol 48 (2) ◽  
pp. 485-498 ◽  
Author(s):  
Ch. G. Philos ◽  
I. K. Purnaras ◽  
Y. G. Sficas
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Order Linear ◽  
Autonomous Case ◽  
Unstable Type ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractSecond-order linear (non-autonomous as well as autonomous) delay differential equations of unstable type are considered. In the non-autonomous case, sufficient conditions are given in order that all oscillatory solutions are bounded or all oscillatory solutions tend to zero at $\infty$. In the case where the equations are autonomous, necessary and sufficient conditions are established for all oscillatory solutions to be bounded or all oscillatory solutions to tend to zero at $\infty$.

scholarly journals Solving Oscillatory Delay Differential Equations Using Block Hybrid Methods

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Sufia Zulfa Ahmad ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Hybrid Methods ◽  
Second Order ◽  
Order Conditions ◽  
Order Condition ◽  
Oscillatory Solutions ◽  
Cpu Time ◽  
Delay Differential

A set of order condition for block explicit hybrid method up to order five is presented and, based on the order conditions, two-point block explicit hybrid method of order five for the approximation of special second order delay differential equations is derived. The method is then trigonometrically fitted and used to integrate second-order delay differential equations with oscillatory solutions. The efficiency curves based on the log of maximum errors versus the CPU time taken to do the integration are plotted, which clearly demonstrated the superiority of the trigonometrically fitted block hybrid method.

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

Symmetry ◽  
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.

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

Mathematics ◽  
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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