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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 38, Issue 2, 2019, pp. 157–189**

**DOI: 10.4171/ZAA/1633**

Published online: 2019-04-09

On Stability of Delay Equations with Positive and Negative Coefficients with Applications

Leonid Berezansky^{[1]}and Elena Braverman

^{[2]}(1) Ben-Gurion University of the Negev, Beer-Sheva, Israel

(2) University of Calgary, Canada

We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms $$\dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))- \sum_{k=1}^l b_k(t)x(g_k(t))=0$$ and its modifications, and apply them to investigate local stability of Mackey–Glass type models $$\dot{x}(t)=r(t)\left[\beta\frac{x(g(t))}{1+x^n(g(t))}-\gamma x(h(t))\right]$$ and $$\dot{x}(t)=r(t)\left[\beta\frac{x(g(t))}{1+x^n(h(t))}-\gamma x(t)\right],$$

*Keywords: *Variable and distributed delays, positive and negative coefficients, exponential stability, Mackey{Glass equation, solution estimates, local stability.

Berezansky Leonid, Braverman Elena: On Stability of Delay Equations with Positive and Negative Coefficients with Applications. *Z. Anal. Anwend.* 38 (2019), 157-189. doi: 10.4171/ZAA/1633