Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Period two implies all periods for a class of ODEs: A multivalued map approach


Authors: Jan Andres, Tomás Fürst and Karel Pastor
Journal: Proc. Amer. Math. Soc. 135 (2007), 3187-3191
MSC (2000): Primary 34A60, 34C25, 37E05, 47H04
Published electronically: February 28, 2007
MathSciNet review: 2322749
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present an elementary proof that, for a multivalued map $ \varphi:\mathbb{R}\multimap \mathbb{R}$ with nonempty connected values and monotone margins, the existence of a periodic orbit of any order $ k>1$ implies the existence of periodic orbits of all orders. This generalizes a very recent result of this type in terms of scalar ordinary differential equations without uniqueness, due to F. Obersnel and P. Omari, obtained by means of lower and upper solutions techniques.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34A60, 34C25, 37E05, 47H04

Retrieve articles in all journals with MSC (2000): 34A60, 34C25, 37E05, 47H04


Additional Information

Jan Andres
Affiliation: Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
Email: andres@inf.upol.cz

Tomás Fürst
Affiliation: Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
Email: tomas.furst@seznam.cz

Karel Pastor
Affiliation: Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
Email: pastor@inf.upol.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08885-5
PII: S 0002-9939(07)08885-5
Keywords: Periodic orbits, multivalued maps, monotone margins, Sharkovskii's theorem, ordinary differential equations without uniqueness, subharmonic solutions.
Received by editor(s): June 14, 2006
Published electronically: February 28, 2007
Additional Notes: This work was supported by the Council of Czech Government (MSM 6198959214).
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society