Estimation of Periodic Solutions Number of First-Order Differential Equations

Research outputpeer-review

8 Citations (Scopus)

Abstract

The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions.

Original languageEnglish
Title of host publication8th Polyakhov's Reading
Subtitle of host publicationProceedings of the International Scientific Conference on Mechanics
EditorsElena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina
PublisherAmerican Institute of Physics
Number of pages5
Volume1959
ISBN (Electronic)9780735416604
DOIs
Publication statusPublished - 2018
EventInternational Scientific Conference on Mechanics: 8th Polyakhov's Reading - Saint Petersburg
Duration: 29 Jan 20182 Feb 2018

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1959
ISSN (Print)0094-243X

Conference

ConferenceInternational Scientific Conference on Mechanics: 8th Polyakhov's Reading
CountryRussian Federation
CitySaint Petersburg
Period29/01/182/02/18

Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ivanov, G., Alferov, G., Gorovenko (Efimova), P., & Sharlay, A. (2018). Estimation of Periodic Solutions Number of First-Order Differential Equations. In E. V. Kustova, G. A. Leonov, M. P. Yushkov, N. F. Morosov, & M. A. Mekhonoshina (Eds.), 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics (Vol. 1959). [080006] (AIP Conference Proceedings; Vol. 1959). American Institute of Physics. https://doi.org/10.1063/1.5034723
Ivanov, Gennady ; Alferov, Gennady ; Gorovenko (Efimova), Polina ; Sharlay, Artem. / Estimation of Periodic Solutions Number of First-Order Differential Equations. 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. editor / Elena V. Kustova ; Gennady A. Leonov ; Mikhail P. Yushkov ; Nikita F. Morosov ; Mariia A. Mekhonoshina. Vol. 1959 American Institute of Physics, 2018. (AIP Conference Proceedings).
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abstract = "The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions.",
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Ivanov, G, Alferov, G, Gorovenko (Efimova), P & Sharlay, A 2018, Estimation of Periodic Solutions Number of First-Order Differential Equations. in EV Kustova, GA Leonov, MP Yushkov, NF Morosov & MA Mekhonoshina (eds), 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. vol. 1959, 080006, AIP Conference Proceedings, vol. 1959, American Institute of Physics, Saint Petersburg, 29/01/18. https://doi.org/10.1063/1.5034723

Estimation of Periodic Solutions Number of First-Order Differential Equations. / Ivanov, Gennady; Alferov, Gennady; Gorovenko (Efimova), Polina; Sharlay, Artem.

8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. ed. / Elena V. Kustova; Gennady A. Leonov; Mikhail P. Yushkov; Nikita F. Morosov; Mariia A. Mekhonoshina. Vol. 1959 American Institute of Physics, 2018. 080006 (AIP Conference Proceedings; Vol. 1959).

Research outputpeer-review

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T1 - Estimation of Periodic Solutions Number of First-Order Differential Equations

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AU - Sharlay, Artem

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N2 - The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions.

AB - The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions.

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Ivanov G, Alferov G, Gorovenko (Efimova) P, Sharlay A. Estimation of Periodic Solutions Number of First-Order Differential Equations. In Kustova EV, Leonov GA, Yushkov MP, Morosov NF, Mekhonoshina MA, editors, 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. Vol. 1959. American Institute of Physics. 2018. 080006. (AIP Conference Proceedings). https://doi.org/10.1063/1.5034723