EUDML

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $\dot{x} (t) + \sum_{k = 1}^{m} a_{k} (t) x (h_{k} (t)) = 0, a_{k} (t) \geq 0$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.

On stability of linear neutral differential equations with variable delays

Leonid Berezansky; Elena Braverman — 2019

Czechoslovak Mathematical Journal

We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $\dot{x} (t) - a (t) \dot{x} (g (t)) + b (t) x (h (t)) = 0,$ where $| a (t) | < 1, b (t) \geq 0, h (t) \leq t, g (t) \leq t,$ and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

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Oscillation for equations with positive and negative coefficients and distributed delay. II: Applications.

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Exponential stability of difference equations with several delays: recursive approach.

Preservation of exponential stability for equations with several delays

On stability of linear neutral differential equations with variable delays