On Multivalent Guiding Functions Method in the Periodic Problem for Random Differential Equations

Abstract

By applying the random topological degree theory we develop the methods of random multivalent guiding functions and use them for the study of periodic solutions for random differential equations in finite dimensional spaces.

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Acknowledgements

The authors are grateful to the anonymous referees for their helpful remarks. The work on the paper was carried out during Prof. V. Obukhovskii’s and Prof. S. Kornev’s visit to Dipartimento di Matematica e Informatica “Ulisse Dini”, Universita di Firenze, Firenze, Italy in 2017. They would like to express their gratitude to the members of the Dipartimento di Matematica e Informatica “Ulisse Dini” for their kind hospitality.

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Correspondence to Valeri Obukhovskii.

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The work is supported by the Ministry of Education and Science of the Russian Federation in the frameworks of the project part of the state work quota (Project No. 1.3464.2017/4.6) and from INDAM and the University of Firenze. The third author is partially supported by GNANPA and the University of Firenze (Italy).

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Kornev, S., Obukhovskii, V. & Zecca, P. On Multivalent Guiding Functions Method in the Periodic Problem for Random Differential Equations. J Dyn Diff Equat 31, 1017–1028 (2019). https://doi.org/10.1007/s10884-019-09734-5

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Keywords

  • Random differential equation
  • Random topological degree
  • Random multivalent guiding function

Mathematics Subject Classification

  • 34F05
  • 34A34
  • 34C25