A version of Sharkovskii’s theorem for differential equations
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- by Jan Andres and Karel Pastor
- Proc. Amer. Math. Soc. 133 (2005), 449-453
- DOI: https://doi.org/10.1090/S0002-9939-04-07627-0
- Published electronically: August 30, 2004
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Abstract:
We present a version of the Sharkovskii cycle coexistence theorem for differential equations. Our earlier applicable version is extended here to hold with the exception of at most two orbits. This result, which (because of counter-examples) cannot be improved, is then applied to ordinary differential equations and inclusions. In particular, if a time-periodic differential equation has $n$-periodic solutions with $n \not = 2^m$, for all $m \in {\mathbb N}$, then infinitely many subharmonics coexist.References
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Bibliographic Information
- Jan Andres
- Affiliation: Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
- MR Author ID: 222871
- Email: andres@risc.upol.cz
- Karel Pastor
- Affiliation: Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
- Email: pastor@inf.upol.cz
- Received by editor(s): September 3, 2003
- Published electronically: August 30, 2004
- Additional Notes: Supported by the Council of Czech Government (J14/98:153100011)
- Communicated by: Carmen C. Chicone
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 449-453
- MSC (2000): Primary 34C25, 34A60, 37E05, 47H04
- DOI: https://doi.org/10.1090/S0002-9939-04-07627-0
- MathSciNet review: 2093067