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

G. V. Demidenko

doi:10.1134/S1995080222020044

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

G. V. Demidenko

Differential Equations Section

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

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.

Original language	English
Article number	3
Pages (from-to)	3336-3343
Number of pages	8
Journal	Lobachevskii Journal of Mathematics
Volume	42
Issue number	14
DOIs	https://doi.org/10.1134/S1995080222020044
Publication status	Published - Dec 2021

Keywords

exponential dichotomy
Lyapunov equation
periodic solutions
projectors
Sobolev spaces

OECD FOS+WOS

1.01 MATHEMATICS

State classification of scientific and technological information

27 MATHEMATICS

Access to Document

10.1134/S1995080222020044

Cite this

@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",

}

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

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 -

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

Abstract

Keywords

OECD FOS+WOS

State classification of scientific and technological information

Access to Document

Other files and links

Fingerprint

Cite this