## A generalization of Bendixson’s criterion

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- by Michal Fečkan PDF
- Proc. Amer. Math. Soc.
**129**(2001), 3395-3399 Request permission

## 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.## References

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## Additional Information

**Michal Fečkan**- Affiliation: Department of Mathematical Analysis, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
- Email: Michal.Feckan@fmph.uniba.sk
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**129**(2001), 3395-3399 - MSC (2000): Primary 34A34, 34C40, 37C10
- DOI: https://doi.org/10.1090/S0002-9939-01-06107-X
- MathSciNet review: 1845018