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 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 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.

ON STABILITY OF THE SECOND ORDER DELAY DIFFERENTIAL EQUATION: THREE METHODS

2021 ◽  
Vol 28 (1-2) ◽  
pp. 3-17
Author(s):  
LEONID BEREZANSKY
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Second Order ◽  
Operator Equations ◽  
Linear Delay ◽  
Delay Differential

The aim of the paper is a review of some methods on exponential stability for linear delay differential equations of the second order. All these methods are based on Bohl-Perron theorem which reduces stability investi-gations to study the properties of operator equations in some functional spaces. As an example of application of these methods we consider the following equation x¨(t)+ a(t)˙x(g(t)) + b(t)x(h(t)) = 0.

scholarly journals Oscillatory results for second-order noncanonical delay differential equations

2019 ◽  
Vol 39 (4) ◽  
pp. 483-495 ◽  
Author(s):  
Jozef Džurina ◽  
Irena Jadlovská ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Positive Solutions ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Second Order ◽  
Linear Delay ◽  
Delay Differential

The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation \[\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,\] under the condition \[\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt \infty.\] Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.

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 On the oscillation of third-order quasi-linear delay differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Tongxing Li ◽  
Chenghui Zhang ◽  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
The Third ◽  
Linear Delay ◽  
Delay Differential

Abstract The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation , (E) where and τ(t) ≤ t. We establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.

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