Global existence without uniqueness

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1970 English Publisher:Springer Science and Business Media LLCJournal:Annali di Matematica Pura ed Applicata, volume 87, pages 227-236 (issn: 0373-3114, eissn: 1618-1891,

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Authors: Bernfeld, Stephen R.;

doi: 10.1007/bf02411978

Global existence without uniqueness

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Abstract

In this paper we investigate the extendability of solutions of ordinary differential equations on [to, ∞) with the use of Liapunov functions. The results extend to non-unique systems the work done by Conti and Strauss, as well as establishing an equivalence between two properties of a Liapunov function.

Keywords

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Stability of solutions to ordinary differential equations

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