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

Oscillation Theory ◽

Order Linear ◽

The Real ◽

First Order ◽

Linear Delay ◽

Long Time ◽

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.

Infinite integral conditions for oscilation of first order linear delay differential equations with positive and negative coefficients

Bayero Journal of Pure and Applied Sciences ◽

10.4314/bajopas.v11i2.24 ◽

2019 ◽

Vol 11 (2) ◽

pp. 186

Author(s):

A. Tahir ◽

Y. Haruna

Keyword(s):

Differential Equations ◽

Integral Conditions ◽

Order Linear ◽

First Order ◽

Positive And Negative Coefficients ◽

Linear Delay ◽

Infinite Integral ◽

An Oscillation Criterion for First Order Linear Delay Differential Equations

Canadian Mathematical Bulletin ◽

10.4153/cmb-1998-030-3 ◽

1998 ◽

Vol 41 (2) ◽

pp. 207-213 ◽

Cited By ~ 13

Author(s):

CH. G. Philos ◽

Y. G. Sficas

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Delay Differential Equation ◽

Oscillation Criterion ◽

Order Linear ◽

First Order ◽

Linear Delay ◽

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 .

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

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106366 ◽

2020 ◽

Vol 106 ◽

pp. 106366 ◽

Cited By ~ 1

Author(s):

Ábel Garab ◽

Ioannis P. Stavroulakis

Keyword(s):

Differential Equations ◽

Oscillation Criteria ◽

Order Linear ◽

First Order ◽

Variable Delays ◽

Linear Delay ◽

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

Baghdad Science Journal ◽

10.21123/bsj.8.3.806-809 ◽

2011 ◽

Vol 8 (3) ◽

pp. 806-809

Author(s):

Baghdad Science Journal

Keyword(s):

Differential Equations ◽

Sufficient Conditions ◽

Oscillation Criteria ◽

Order Linear ◽

First Order ◽

Positive And Negative Coefficients ◽

All Solutions ◽

Linear Delay ◽

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.

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

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500027372 ◽

1998 ◽

Vol 128 (6) ◽

pp. 1371-1387 ◽

Cited By ~ 13

Author(s):

Ch. G. Philos

Keyword(s):

Differential Equations ◽

Asymptotic Behaviour ◽

Characteristic Equation ◽

Trivial Solution ◽

Order Linear ◽

First Order ◽

Linear Delay ◽

The Stability ◽

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.

Superconvergence of a Dg Method for First-Order Linear Delay Differential Equations

Journal of Computational Mathematics ◽

10.4208/jcm.1107-m3433 ◽

2011 ◽

Vol 29 (5) ◽

pp. 574-588 ◽

Cited By ~ 17

Author(s):

Dongfang Li and Chengjian Zhang

Keyword(s):

Differential Equations ◽

Order Linear ◽

First Order ◽

Linear Delay ◽

Dg Method ◽

On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations

Archiv der Mathematik ◽

10.1007/s000130050290 ◽

1998 ◽

Vol 71 (6) ◽

pp. 454-464 ◽

Cited By ~ 18

Author(s):

I.-G. E. Kordonis ◽

N.T. Niyianni ◽

C.G. Philos

Keyword(s):

Differential Equations ◽

Neutral Delay ◽

Order Linear ◽

First Order ◽

Neutral Delay Differential Equations ◽

A result on the behavior of the solutions for scalar first order linear autonomous neutral delay differential equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004105008960 ◽

2006 ◽

Vol 140 (02) ◽

pp. 349 ◽

Cited By ~ 5

Author(s):

CH. G. PHILOS ◽

I. K. PURNARAS

Keyword(s):

Differential Equations ◽

Neutral Delay ◽

Order Linear ◽

First Order ◽

Neutral Delay Differential Equations ◽

Oscillations of second order linear delay differential equations

Applicable Analysis ◽

10.1080/00036818808839726 ◽

1988 ◽

Vol 27 (1-3) ◽

pp. 109-123 ◽

Cited By ~ 1

Author(s):

M.R.S. Kulenvić ◽

G. Ladas ◽

Y.G. Sficas

Keyword(s):

Differential Equations ◽

Second Order ◽

Order Linear ◽

Linear Delay ◽

Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

Abstract and Applied Analysis ◽

10.1155/2013/281581 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Fatima N. Ahmed ◽

Rokiah Rozita Ahmad ◽

Ummul Khair Salma Din ◽

Mohd Salmi Md Noorani

Keyword(s):

Differential Equations ◽

Sufficient Conditions ◽

Neutral Delay ◽

Oscillation Criteria ◽

Order Linear ◽

First Order ◽

All Solutions ◽

Neutral Delay Differential Equations ◽

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.