Description

• Title:
  Sharkovskii's theorem, differential inclusions, and beyond
• Creator:
  Andres, Jan;
  Fürst, Tomáš;
  Pastor, Karel
• Description:
  We explain why the Poincaré translation operators along the trajectories of upper-Carathéodory differential inclusions do not satisfy the exceptional cases, described in our earlier counter-examples, for upper semicontinuous maps. Such a discussion was stimulated by a recent paper of F. Obersnel and P. Omari, where they show that, for Carathéodory scalar differential equations, the existence of just one subharmonic solution (e.g of order $2$) implies the existence of subharmonics of all orders. We reprove this result alternatively just via a multivalued Poincaré translation operator approach. We also establish its randomized version on the basis of a universal randomization scheme developed recently by the first author.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 1 (March 2009); 149 - 168;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.011/8650
• Subject:
  Sharkovskiĭ-type theorems;
  multivalued maps with monotone margins;
  Poincarĭé translation operators;
  coexistence of infinitely many periodic solutions;
  no exceptions;
  deterministic and random differential inclusions;
  random periodic solutions;
  34A60;
  37E05;
  37E15;
  37H10;
  47H04;
  47H40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.011
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other