On differential equations with state-dependent delay : the principles of linearized stability and instability revisited

Stumpf Eugen: On differential equations with state-dependent delay : the principles of linearized stability and instability revisited. (2016)

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Abstract

This paper deals with a dynamical systems approach for studying nonlinear autonomous differential equations with bounded state-dependent delay. Starting with the semiflow generated by solutions of such an equation, we revisit the principles of linearized stability and instability enabling the local stability analysis of equilibria via linearization. In particular, we prove both principles in an elementary way by using only a quantitative version of continuous dependence of the semiflow on initial data together with basic properties of the discrete semi-dynamical system induced by iterations of some time-t-map.

Item Type: Journal
Other title: Honoring the career of Tibor Krisztin on the occasion of his sixtieth birthday
Publication full: Electronic journal of qualitative theory of differential equations : special edition
Date: 2016
Volume: 2
Number: 81
ISSN: 1417-3875
Number of Pages: 17
Language: English
DOI: 10.14232/ejqtde.2016.1.81
Uncontrolled Keywords: Differenciálegyenlet - késleltetett
Additional Information: Bibliogr.: p. 15-17. ; összefoglalás angol nyelven
Date Deposited: 2021. Nov. 11. 14:59
Last Modified: 2021. Nov. 12. 09:42
URI: http://acta.bibl.u-szeged.hu/id/eprint/73748

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