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Bendixson's criterion for systems with non-C1 vector fields

Published online by Cambridge University Press:  12 July 2007

Zhanyuan Hou
Zhanyuan Hou
Affiliation:
Department of Computing, Information Systems and Mathematics, London Guildhall University, 100 Minories, London EC3N 1JY, UK
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Abstract

The generalized Bendixson's criterion for non-existence of non-constant periodic solutions of an autonomous system dx/dt = f(x), x ∈ D, is further extended to systems when the condition f ∈ C1(D, RN) is violated. In particular, the criterion can be applied to region-wise linear systems in RN.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 2 , April 2003 , pp. 393 - 407
Copyright
Copyright © Royal Society of Edinburgh 2003

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