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A generalization of Bendixson's criterion


Author: Michal Feckan
Journal: Proc. Amer. Math. Soc. 129 (2001), 3395-3399
MSC (2000): Primary 34A34, 34C40, 37C10
Published electronically: April 25, 2001
MathSciNet review: 1845018
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Abstract:

Bendixson's condition on the nonexistence of periodic solutions for planar ordinary differential equations is extended to higher dimensional ordinary differential equations with first integrals to preclude the existence of certain invariant Lipschitz compact submanifolds for those equations.


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Additional Information

Michal Feckan
Affiliation: Department of Mathematical Analysis, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
Email: Michal.Feckan@fmph.uniba.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06107-X
Keywords: Invariant submanifolds, first integrals, flows
Received by editor(s): April 10, 2000
Published electronically: April 25, 2001
Additional Notes: This work was supported by Grant GA-MS 1/6179/00.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2001 American Mathematical Society