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Randomized Sharkovsky-type results and random subharmonic solutions of differential inclusions


Authors: Jan Andres and Paweł Barbarski
Journal: Proc. Amer. Math. Soc. 144 (2016), 1971-1983
MSC (2010): Primary 37H10, 47H40; Secondary 37E05, 37E15, 47H04
DOI: https://doi.org/10.1090/proc/13014
Published electronically: January 26, 2016
MathSciNet review: 3460160
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Abstract: Two multivalued deterministic versions of the celebrated Sharkovsky cycle coexistence theorem are randomized in terms of very general random periodic orbits. It is also shown that nontrivial subharmonics of scalar random upper-Carathéodory differential inclusions imply the coexistence of random subharmonics of all orders.


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Additional Information

Jan Andres
Affiliation: Department of Mathematical Analysis and Application of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
Email: jan.andres@upol.cz

Paweł Barbarski
Affiliation: Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
Email: barbarski.pawel@gmail.com

DOI: https://doi.org/10.1090/proc/13014
Keywords: Randomization, Sharkovsky's Theorem, multivalued maps, selection theorems, Suslin space, Suslin family, random operators, random orbits, random differential inclusions, subharmonic solutions, Poincar{\'e} operator
Received by editor(s): May 7, 2015
Published electronically: January 26, 2016
Additional Notes: The work of the first author was supported by the grant 14-06958S “Singularities and impulses in boundary value problems for nonlinear ordinary differential equations” of the Grant Agency of the Czech Republic and the work of the second author by the Foundation for the Polish Science grant MPD/2009-3/4.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society

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