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2019 Explicit stability tests for linear neutral delay equations using infinite series
Leonid Berezansky, Elena Braverman
Rocky Mountain J. Math. 49(2): 387-403 (2019). DOI: 10.1216/RMJ-2019-49-2-387

Abstract

We obtain new, explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays $ (x(t)-a(t)x(g(t)))'+b(t)x(h(t))=0, $ where $|a(t)| \leq A_0 \lt 1$, $0\lt b_0\leq b(t)\leq B_0$, assuming that all parameters of the equation are measurable functions. To analyze the exponential stability, we apply the Bohl-Perron theorem and a reduction of a neutral equation to an equation with an infinite number of non-neutral delay terms. This method has never before been used for this neutral equation; its application allows omitting a usual restriction $|a(t)|\lt {1}/{2}$ in known asymptotic stability tests and the consideration of variable delays.

Funding Statement

This research was partially supported by NSERC, grant No. RGPIN-2015-05976.

Citation

Download Citation

Leonid Berezansky. Elena Braverman. "Explicit stability tests for linear neutral delay equations using infinite series." Rocky Mountain J. Math. 49 (2) 387 - 403, 2019. https://doi.org/10.1216/RMJ-2019-49-2-387

Information

Received: 8 July 2018; Revised: 6 September 2018; Published: 2019
First available in Project Euclid: 23 June 2019

zbMATH: 07079975
MathSciNet: MR3973231
Digital Object Identifier: 10.1216/RMJ-2019-49-2-387

Subjects:
Primary: 34K06, 34K20, 34K40

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 2 • 2019
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