Description

• Title:
  On a multivalued version of the Sharkovskii theorem and its application to differential inclusions, III
• Creator:
  Andres, Jan;
  Pastor, Karel
• Description:
  An extension of the celebrated Sharkovskiĭ cycle coexisting theorem (see [< i> Coexistence of cycles of a continuous map of a line into itself< /i> , Ukrain. Math. J. < b> 16< /b> (1964), 61–71]) is given for (strongly) admissible multivalued self-maps in the sense of [L. Górniewicz, < i> Topological Fixed Point Theory of Multivalued Mappings< /i> , Kluwer, Dordrecht, 1999], on a Cartesian product of linear continua. Vectors of admissible self-maps have a triangular structure as in [[P. E. Kloeden, < i> On Sharkovsky’s cycle coexisting ordering< /i> , Bull. Austral. Math. Soc. < b> 20< /b> (1979), 171–177]. Thus, we make a joint generalization of the results in [J. Andres, J. Fišer and L. Jüttner, < i> On a multivalued version of the Sharkovskiĭ theorem and its application to differential inclusions< /i> , Set-Valued Anal. < b> 10< /b> (2002), 1–14], [J. Andres and L. Jüttner, < i> Period three plays a negative role in a multivalued version of Sharkovskiĭ’s theorem< /i> , Nonlinear Anal. < b> 51< /b> (2002), 1101–1104], [J. Andres, L. Jüttner and K. Pastor, < i> On a multivalued version of the Sharkovskiĭ theorem and its application to differential inclusions II< /i> ] (a multivalued case), in [P. E. Kloeden, < i> On Sharkovsky’s cycle coexisting ordering< /i> , Bull. Austral. Math. Soc. < b> 20< /b> (1979), 171–177] (a multidimensional case), and in [H. Schirmer, < i> A topologist’s view of Sharkovskiĭ’s theorem< /i> , Houston, J. Math. < b> 11< /b> (1985), 385–395] (a linear continuum case). The obtained results can be applied, unlike in the single-valued case, to differential equations and inclusions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 22, No 2 (December 2003); 369 - 386;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.046/9584
• Subject:
  Sharkovskiĭ theorem;
  multivalued version;
  multidimensional version;
  linear continuum setting;
  infinitely many orbits;
  subharmonics of differential systems;
  34A60;
  37E05;
  47H04;
  47H10;
  58C30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.046
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other