scholarly journals Existence of Oscillatory Solutions of Second Order Delay Differential Equations with Distributed Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Youjun Liu ◽  
Jianwen Zhang ◽  
Jurang Yan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Deviating Arguments ◽  
Distributed Deviating Arguments ◽  
Delay Differential

scholarly journals Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. T. Ademola ◽  
B. S. Ogundare ◽  
M. O. Ogundiran ◽  
O. A. Adesina
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Lyapunov Functional ◽  
Second Order ◽  
Asymptotically Stable ◽  
Boundedness Of Solutions ◽  
Deviating Arguments ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results.

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.

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