scholarly journals A computer assisted proof of multiple periodic orbits in some first order non-linear delay differential equation

2016 ◽  
pp. 1-19 ◽  
Author(s):  
Robert Szczelina
Keyword(s):  
Differential Equation ◽  
Periodic Orbits ◽  
Delay Differential Equation ◽  
Computer Assisted ◽  
First Order ◽  
Computer Assisted Proof ◽  
Linear Delay ◽  
Non Linear ◽  
Multiple Periodic Orbits ◽  
Delay Differential

scholarly journals New Oscillation and Nonoscillation Criteria for a Class of Linear Delay Differential Equation

2019 ◽  
Vol 8 (10) ◽  
pp. 308-313
Keyword(s):  
Differential Equation ◽  
Continuous Function ◽  
Delay Differential Equation ◽  
Sufficient Condition ◽  
First Order ◽  
Linear Delay ◽  
Piecewise Continuous ◽  
Delay Differential ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation

In this article the authors established sufficient condition for the first order delay differential equation in the form , ( ) where , = and is a non negative piecewise continuous function. Some interesting examples are provided to illustrate the results. Keywords: Oscillation, delay differential equation and bounded. AMS Subject Classification 2010: 39A10 and 39A12.

An Oscillation Criterion for First Order Linear Delay Differential Equations

1998 ◽  
Vol 41 (2) ◽  
pp. 207-213 ◽  
Author(s):  
CH. G. Philos ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillation Criterion ◽  
Order Linear ◽  
First Order ◽  
Linear Delay ◽  
Delay Differential

AbstractA new oscillation criterion is given for the delay differential equation , where and the function T defined by is increasing and such that . This criterion concerns the case where .

scholarly journals Oscillation tests for first-order linear differential equations with non-monotone delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Emad R. Attia
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Linear Differential Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Delay ◽  
Linear Differential ◽  
A New Technique ◽  
Delay Differential

AbstractWe study the oscillation of a first-order linear delay differential equation. A new technique is developed and used to obtain new oscillatory criteria for differential equation with non-monotone delay. Some of these results can improve many previous works. An example is introduced to illustrate the effectiveness and applicability of our results.

scholarly journals Oscillation of First Order Linear Delay Differential Equation with Variable Coefficients

2019 ◽  
Vol 8 (3) ◽  
pp. 1499-1508
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Positive Constant ◽  
Variable Coefficients ◽  
Sufficient Condition ◽  
Order Linear ◽  
First Order ◽  
Variable Delays ◽  
Linear Delay ◽  
Delay Differential

In this article the authors established sufficient condition for the oscillation of the first order linear delay differential equation ( * ) where is a positive constant, with several variable delays. Some interesting examples are provided to illustrate the results.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

Variation formulas of solution for a delay differential equation taking into account delay perturbation and the continuous initial condition

2011 ◽  
Vol 18 (2) ◽  
pp. 345-364
Author(s):  
Tamaz Tadumadze
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Delay Differential Equation ◽  
Initial Function ◽  
Initial Moment ◽  
Initial Condition ◽  
Constant Delay ◽  
Non Linear ◽  
Linear Differential ◽  
Delay Differential

Abstract Variation formulas of solution are proved for a non-linear differential equation with constant delay. In this paper, the essential novelty is the effect of delay perturbation in the variation formulas. The continuity of the initial condition means that the values of the initial function and the trajectory always coincide at the initial moment.

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