The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (426 KB) | Metadata | Table of Contents | ZAA summary
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