Set-Valued Analysis

, Volume 10, Issue 1, pp 1–14 | Cite as

On a Multivalued Version of the Sharkovskii Theorem and its Application to Differential Inclusions

  • J. Andres
  • J. Fišer
  • L. Jüttner

Abstract

Motivated by the applications to differential equations without uniqueness conditions, we separately prove multivalued versions of the celebrated Sharkovskii and Li–Yorke theorems. These are then applied, via multivalued Poincaré operators, to Carathéodory differential inclusions. Thus, besides another, infinitely many subharmonics of all integer orders can be obtained. Unlike in the single-valued case, for example, period three brings serious obstructions. Three counter-examples, related to these complications, are therefore presented as well. In a multivalued setting, new phenomena are so exhibited.

Sharkovskii theorem Li–Yorke theorem periodic orbits subharmonics multivalued version differential inclusions multiplicity results 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • J. Andres
    • 1
  • J. Fišer
    • 1
  • L. Jüttner
    • 1
  1. 1.Department of Mathematical Analysis, Faculty of SciencePalacký UniversityOlomouc–HejčínCzech Republic

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