# A new stability test for linear neutral differential equations

**Authors:** Leonid Berezansky, Elena Braverman

arXiv: 1902.08249 · 2019-02-25

## TL;DR

This paper introduces new explicit exponential stability criteria for linear scalar neutral differential equations with two bounded delays, utilizing the Bohl-Perron theorem and a transformation approach, with applications to neutral logistic equations.

## Contribution

The paper presents novel explicit stability conditions for neutral differential equations with delays, expanding the theoretical understanding and practical criteria for stability analysis.

## Key findings

- Derived new exponential stability conditions for neutral equations
- Applied results to neutral logistic equations
- Provided explicit criteria using Bohl-Perron theorem

## Abstract

We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays $ \dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0, $ where $ 0\leq a(t)\leq A_0<1$, $0<b_0\leq b(t)\leq B$, using the Bohl-Perron theorem and a transformation of the neutral equation into a differential equation with an infinite number of delays. The results are applied to the neutral logistic equation.

## Full text

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## References

17 references — full list in the complete paper: https://tomesphere.com/paper/1902.08249/full.md

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Source: https://tomesphere.com/paper/1902.08249