scholarly journals The MID property for a second-order neutral time-delay differential equation

2020 ◽  
Author(s):  
Amina Benarab ◽  
Islam Boussaada ◽  
Karim Trabelsi ◽  
Guilherme Mazanti ◽  
Catherine Bonnet
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Second Order ◽  
Delay Differential

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.

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

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