scholarly journals Oscillation criteria for first order linear delay differential equations with several variable delays

2020 ◽  
Vol 106 ◽  
pp. 106366 ◽  
Author(s):  
Ábel Garab ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Variable Delays ◽  
Linear Delay ◽  
Delay Differential

scholarly journals Oscillations of First Order Linear Delay Differential Equations with positive and negative coefficients

2011 ◽  
Vol 8 (3) ◽  
pp. 806-809
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.

scholarly journals Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. Some examples are inserted to illustrate our results.

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 Explicit values of the oscillation bounds for linear delay differential equations with monotone argument

2021 ◽  
Author(s):  
Mihály Pituk ◽  
Ioannis P. Stavroulakis ◽  
John Ioannis Stavroulakis
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillation Theory ◽  
Order Linear ◽  
The Real ◽  
First Order ◽  
Linear Delay ◽  
Long Time ◽  
Delay Differential

The problem of finding the oscillation bounds for first-order linear delay differential equations has been in the focus of the oscillation theory for a long time. Although numerous estimates for the oscillation bounds are available in the literature, their explicit values were not known. In this paper, we give the oscillation bounds explicitly in terms of the real branches of the Lambert [Formula: see text] function.

Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations

1998 ◽  
Vol 128 (6) ◽  
pp. 1371-1387 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Characteristic Equation ◽  
Trivial Solution ◽  
Delay Differential Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Delay ◽  
The Stability ◽  
Delay Differential

First-order scalar linear delay differential equations with periodic coefficients and constant delays are considered, where the coefficients have a common period and the delays are multiples of this period. A basic asymptotic criterion is given. Moreover, some results on the nonoscillation and on the stability of the trivial solution are obtained. An equation, which is in a sense the characteristic equation, plays an important role in establishing the results of the paper.

scholarly journals Oscillation Criteria of First Order Neutral Delay Differential Equations with Variable Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new oscillation criteria are given for first order neutral delay differential equations with variable coefficients. Our results generalize and extend some of the well-known results in the literature. Some examples are considered to illustrate the main results.

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