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Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 2127–2144 | Cite as

Application of the Randomized Sharkovsky-Type Theorems to Random Impulsive Differential Equations and Inclusions

  • Jan AndresEmail author
Article
  • 70 Downloads

Abstract

Our randomized Sharkovsky-type theorems are applied to random impulsive differential equations and inclusions in order to establish the coexistence of random periodic solutions with various periods, which are forced according to the Sharkovsky ordering of positive integers. The impulses can be single-valued or multivalued and deterministic or random. The obtained theorems can be rather curiously stronger than their deterministic analogies. The relationship to deterministic chaos is also indicated.

Keywords

Sharkovsky-type theorems Random differential equations and inclusions Deterministic and random impulses Coexistence of random periodic solutions Random chaos 

Mathematics Subject Classification

34B37 37E15 47H10 47H40 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký UniversityOlomoucCzech Republic

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