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Izvestiya: Mathematics, 2020, Volume 84, Issue 2, Pages 209–245
DOI: https://doi.org/10.1070/IM8896 (Mi im8896) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A new approach to the question of the existence of bounded solutions of functional differential equations of point type

L. A. Beklaryan

Central Economics and Mathematics Institute Russian Academy of Sciences, Moscow
English version PDF (691 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM8896
Abstract: We develop an approach which we used to deduce conditions of a new type for the existence of periodic solutions of ordinary differential equations and functional differential equations of point type. These conditions are based on the use of asymptotic properties of solutions of differential equations which can be observed on shifts of solutions and stated in terms of averages over the period on a distinguished sphere in the phase space. The development of this approach enables us to obtain conditions for the existence of bounded solutions for the same classes of functional differential equations.
Keywords: functional differential equations, bounded solutions.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00147-а
This paper was written with the support of the Russian Foundation for Basic Research (grant no. 19-01000147-a).
Received: 15.01.2019
Revised: 16.06.2019
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 2, Pages 3–42
DOI: https://doi.org/10.4213/im8896
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 34K13
Language: English
Original paper language: Russian
Citation: L. A. Beklaryan, “A new approach to the question of the existence of bounded solutions of functional differential equations of point type”, Izv. RAN. Ser. Mat., 84:2 (2020), 3–42; Izv. Math., 84:2 (2020), 209–245
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:342
    Russian version PDF:52
    English version PDF:19
    References:37
    First page:11
     
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