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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of Bendixson’s criterion
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by Michal Fečkan PDF
Proc. Amer. Math. Soc. 129 (2001), 3395-3399 Request permission


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 Fečkan
  • Affiliation: Department of Mathematical Analysis, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
  • Email:
  • 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:
  • MathSciNet review: 1845018