Exponential stability of a second order delay differential equation without damping term

2015 ◽  
Vol 258 ◽  
pp. 483-488 ◽  
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Mikhail Gitman ◽  
Valery Stolbov
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Second Order ◽  
Damping Term ◽  
Delay Differential

Nonoscillation and exponential stability of the second order delay differential equation with damping

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Mikhail Gitman ◽  
Valery Stolbov
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Second Order ◽  
Delay Differential

AbstractFor a delay differential equation

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 Criteria for the Oscillation of Solutions to Linear Second-Order Delay Differential Equation with a Damping Term

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 246
Author(s):  
Osama Moaaz ◽  
Elmetwally M. E. Elabbasy ◽  
Jan Awrejcewicz ◽  
Aml Abdelnaser
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Second Order ◽  
Iterative Technique ◽  
Damping Term ◽  
Delay Differential ◽  
New Criterion ◽  
Oscillation Of Solutions

The aim of this work is to present new oscillation results for a class of second-order delay differential equations with damping term. The new criterion of oscillation depends on improving the asymptotic properties of the positive solutions of the studied equation by using an iterative technique. Our results extend some of the results recently published in the literature.

scholarly journals Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
R. Rath ◽  
N. Misra ◽  
L. Padhy
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
T Tau

AbstractIn this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$\left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

scholarly journals Stability Switches and Hopf Bifurcations in a Second-Order Complex Delay Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
M. Roales ◽  
F. Rodríguez
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Second Order ◽  
Delay Equation ◽  
Hopf Bifurcations ◽  
Order Complex ◽  
Stability Switches ◽  
Delay Differential ◽  
Complex Coefficients

The existence of stability switches and Hopf bifurcations for the second-order delay differential equation x′′t+ax′t-τ+bxt=0,  t>0, with complex coefficients, is studied in this paper.

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