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.

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 Robustness of solutions of linear differential equations with infinite delay

2006 ◽  
Vol 2006 ◽  
pp. 1-13
Author(s):  
Anwar A. Al-Badarneh (Al-Nayef) ◽  
Rabaa K. Maaitah
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Infinite Delay ◽  
Nonlinear Perturbation ◽  
Linear Differential Equations ◽  
Solution Operator ◽  
Linear Delay ◽  
Linear Differential ◽  
Delay Differential

We use some consequences of the concept of semihyperbolicity of the solution operator to show robustness of solutions of the linear delay differential equation x′(t)=Ax(t)+Bx(t−r) with infinite delay with respect to a small nonlinear perturbation.

scholarly journals New Stability Conditions for Linear Differential Equations with Several Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Leonid Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Linear Differential Equations ◽  
Stability Conditions ◽  
Linear Delay ◽  
Linear Differential ◽  
Several Delays ◽  
Delay Differential

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equationx˙(t)+∑k=1mak(t)x(hk(t))=0with measurable delays and coefficients. These results are compared to known stability tests.

scholarly journals Oscillation of first order linear differential equations with several non-monotone delays

2018 ◽  
Vol 16 (1) ◽  
pp. 83-94
Author(s):  
E.R. Attia ◽  
V. Benekas ◽  
H.A. El-Morshedy ◽  
I.P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

AbstractConsider the first-order linear differential equation with several retarded arguments$$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

scholarly journals Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term

2019 ◽  
Vol 39 (1) ◽  
pp. 39-47 ◽  
Author(s):  
John R. Graef ◽  
Said R. Grace ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Order Linear ◽  
First Order ◽  
Neutral Term ◽  
Linear Delay ◽  
Even Order ◽  
A New Technique ◽  
Delay Differential

The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.

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.

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

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