Geodesic
On stability of linear neutral differential equations with variable delays
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 863-891.

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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 $$ |a(t)|1, \quad b(t)\geq 0, \quad h(t)\leq t, \quad g(t)\leq t, $$ and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.
DOI : 10.21136/CMJ.2019.0534-17
Classification : 34K06, 34K20, 34K40, 45J05
Keywords: neutral equation; exponential stability; solution estimate; integro-differential equation; distributed delay 
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Berezansky, Leonid; Braverman, Elena. On stability of linear neutral differential equations with variable delays. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 863-891. doi : 10.21136/CMJ.2019.0534-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0534-17/

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