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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Periodic segment implies infinitely many periodic solutions
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by Wacław Marzantowicz and Klaudiusz Wójcik PDF
Proc. Amer. Math. Soc. 135 (2007), 2637-2647 Request permission

Abstract:

In this note we show that the existence of a periodic segment for a non-autonomous ODE with periodic coefficients implies the existence of infinitely many periodic solutions inside this segment provided that a sequence of Lefschetz numbers of iterations of an associated map is not constant. In the case when this sequence is bounded we have to impose a geometric condition on the segment to get solutions by use of symbolic dynamics.
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Additional Information
  • Wacław Marzantowicz
  • Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz Universiy of Poznań, Umultowska 67, 61-614 Poznań, Poland
  • Klaudiusz Wójcik
  • Affiliation: PWSZ Nowy Sa̧cz, Institute of Pedagogy, Ul. Chruślicka 6, 33-300 Nowy Sa̧cz, Poland and Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
  • Received by editor(s): January 2, 2006
  • Received by editor(s) in revised form: April 7, 2006
  • Published electronically: March 21, 2007
  • Additional Notes: The first author’s research was supported by KBN grant 2P03A 03929
  • Communicated by: Carmen C. Chicone
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2637-2647
  • MSC (2000): Primary 54H25, 37B35, 37B55
  • DOI: https://doi.org/10.1090/S0002-9939-07-08750-3
  • MathSciNet review: 2302587