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Instability conditions for solutions of delay systems and localization of limit sets

Instability conditions for solutions of delay systems and localization of limit sets We obtain new tests for the instability of the trivial solutions of equations with deviating argument. In contrast to earlier-known results, these tests use nonmonotone Lyapunov functionals. The class of such functionals contains Lyapunov-Krasovskii functionals as well as Lyapunov-Razumikhin functions as special cases. By localizing the limit sets of solutions, in a number of instability tests, we have been able to drop the requirement that the derivative of the Lyapunov functional according to the system be negative definite. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Instability conditions for solutions of delay systems and localization of limit sets

Differential Equations , Volume 50 (6) – Jul 15, 2014

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266114060032
Publisher site
See Article on Publisher Site

Abstract

We obtain new tests for the instability of the trivial solutions of equations with deviating argument. In contrast to earlier-known results, these tests use nonmonotone Lyapunov functionals. The class of such functionals contains Lyapunov-Krasovskii functionals as well as Lyapunov-Razumikhin functions as special cases. By localizing the limit sets of solutions, in a number of instability tests, we have been able to drop the requirement that the derivative of the Lyapunov functional according to the system be negative definite.

Journal

Differential EquationsSpringer Journals

Published: Jul 15, 2014

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