On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations

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On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations. / Demidenko, G. V.

In: Lobachevskii Journal of Mathematics, Vol. 42, No. 14, 3, 12.2021, p. 3336-3343.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{7fc61aa1169b4a65899ca689214e9429,

title = "On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations",

abstract = "A class of systems of nonlinear differential equations is considered. It is assumed that the linear part of the system has constant coefficients and is exponentially dichotomous. Conditions for the existence of periodic solutions are established and their stability is proved for small perturbations of the coefficients of the linear part and nonlinear terms.",

keywords = "exponential dichotomy, Lyapunov equation, periodic solutions, projectors, Sobolev spaces",

author = "Demidenko, {G. V.}",

note = "Funding Information: The work was supported by the Russian Foundation for Basic Research (project no. 18-29-10086). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = dec,

doi = "10.1134/S1995080222020044",

language = "English",

volume = "42",

pages = "3336--3343",

journal = "Lobachevskii Journal of Mathematics",

issn = "1995-0802",

publisher = "Maik Nauka Publishing / Springer SBM",

number = "14",

}

RIS

TY - JOUR

T1 - On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations

AU - Demidenko, G. V.

PY - 2021/12

Y1 - 2021/12

N2 - A class of systems of nonlinear differential equations is considered. It is assumed that the linear part of the system has constant coefficients and is exponentially dichotomous. Conditions for the existence of periodic solutions are established and their stability is proved for small perturbations of the coefficients of the linear part and nonlinear terms.

AB - A class of systems of nonlinear differential equations is considered. It is assumed that the linear part of the system has constant coefficients and is exponentially dichotomous. Conditions for the existence of periodic solutions are established and their stability is proved for small perturbations of the coefficients of the linear part and nonlinear terms.

KW - exponential dichotomy

KW - Lyapunov equation

KW - periodic solutions

KW - projectors

KW - Sobolev spaces

UR - http://www.scopus.com/inward/record.url?scp=85127314882&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=48154951

UR - https://www.mendeley.com/catalogue/d16a2891-eb03-323a-82b2-3eeada3d568e/

U2 - 10.1134/S1995080222020044

DO - 10.1134/S1995080222020044

M3 - Article

AN - SCOPUS:85127314882

VL - 42

SP - 3336

EP - 3343

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 14

M1 - 3

ER -

ID: 35825589