Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 863-891, 2019


On stability of linear neutral differential equations with variable delays

Leonid Berezansky, Elena Braverman

Received November 24, 2017.   Published online March 22, 2019.

Abstract:  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 $|a(t)|<1$, $b(t)\geq0$, $h(t)\leq t$, $g(t)\leq t$, and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.
Keywords:  neutral equation; exponential stability; solution estimate; integro-differential equation; distributed delay
Classification MSC:  34K40, 34K20, 34K06, 45J05
DOI:  10.21136/CMJ.2019.0534-17


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Affiliations:   Leonid Berezansky, Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: brznsky@math.bgu.ac.il; Elena Braverman, Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada, e-mail: maelena@ucalgary.ca


 
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