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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Liapunov fundtions and global existence without uniqueness


Author: Stephen R. Bernfeld
Journal: Proc. Amer. Math. Soc. 25 (1970), 571-577
MSC: Primary 34.04
MathSciNet review: 0259211
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Abstract: In a recent paper J. Kato and A. Strauss characterized the global existence of solutions of an ordinary differential equation in terms of Liapunov functions in which they assumed the right hand side of the differential equation is locally Lipschitz. In the present paper a characterization of global existence of an ordinary differential equation is found in which the right hand side is merely continuous. The construction of the Liapunov functions depend heavily upon the properties of solution funnels due to the nonuniqueness of solutions.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0259211-1
Keywords: Global existence of solutions, Liapunov functions, nonuniqueness of solutions, solution funnels, initial-value problem
Article copyright: © Copyright 1970 American Mathematical Society