Existence of T/k-Periodic Solutions of a Nonlinear Nonautonomous System Whose Matrix Has a Multiple Eigenvalue

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Existence of T/k-Periodic Solutions of a Nonlinear Nonautonomous System Whose Matrix Has a Multiple Eigenvalue. / Yevstafyeva, V. V.

в: Mathematical Notes, Том 109, № 3-4, 03.2021, стр. 551-562.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{728e7336b16c47079d8c0b8489b9fb54,

title = "Existence of T/k-Periodic Solutions of a Nonlinear Nonautonomous System Whose Matrix Has a Multiple Eigenvalue",

abstract = "Abstract: A system of nth-order ordinary differential equations with relay nonlinearity and periodic perturbation function on the right-hand side is studied. The matrix of the system has real nonzero eigenvalues, among which there is at least one positive and one multiple eigenvalue. A nonsingular transformation that reduces the matrix of the system to Jordan form is used. Continuous periodic solutions with two switching points in the phase space of the system are considered. It is assumed that the period of the perturbation function is a multiple of the periods of these solutions. Necessary conditions for the existence of such solutions are established. An existence theorem for a solution of period equal to the period of the perturbation function is proved. A numerical example confirming the obtained results is presented.",

keywords = "canonical transformation, Jordan matrix, multiple eigenvalue, periodic perturbation function, periodic solution, relay nonlinearity with hysteresis, switching points, system of ordinary differential equations, EQUATIONS, OSCILLATIONS",

author = "Yevstafyeva, {V. V.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = mar,

doi = "10.1134/s0001434621030238",

language = "English",

volume = "109",

pages = "551--562",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "3-4",

}

RIS

TY - JOUR

T1 - Existence of T/k-Periodic Solutions of a Nonlinear Nonautonomous System Whose Matrix Has a Multiple Eigenvalue

AU - Yevstafyeva, V. V.

PY - 2021/3

Y1 - 2021/3

N2 - Abstract: A system of nth-order ordinary differential equations with relay nonlinearity and periodic perturbation function on the right-hand side is studied. The matrix of the system has real nonzero eigenvalues, among which there is at least one positive and one multiple eigenvalue. A nonsingular transformation that reduces the matrix of the system to Jordan form is used. Continuous periodic solutions with two switching points in the phase space of the system are considered. It is assumed that the period of the perturbation function is a multiple of the periods of these solutions. Necessary conditions for the existence of such solutions are established. An existence theorem for a solution of period equal to the period of the perturbation function is proved. A numerical example confirming the obtained results is presented.

AB - Abstract: A system of nth-order ordinary differential equations with relay nonlinearity and periodic perturbation function on the right-hand side is studied. The matrix of the system has real nonzero eigenvalues, among which there is at least one positive and one multiple eigenvalue. A nonsingular transformation that reduces the matrix of the system to Jordan form is used. Continuous periodic solutions with two switching points in the phase space of the system are considered. It is assumed that the period of the perturbation function is a multiple of the periods of these solutions. Necessary conditions for the existence of such solutions are established. An existence theorem for a solution of period equal to the period of the perturbation function is proved. A numerical example confirming the obtained results is presented.

KW - canonical transformation

KW - Jordan matrix

KW - multiple eigenvalue

KW - periodic perturbation function

KW - periodic solution

KW - relay nonlinearity with hysteresis

KW - switching points

KW - system of ordinary differential equations

KW - EQUATIONS

KW - OSCILLATIONS

UR - http://www.scopus.com/inward/record.url?scp=85109162957&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6fd0281f-55a4-3606-92e0-6d88ce814375/

U2 - 10.1134/s0001434621030238

DO - 10.1134/s0001434621030238

M3 - Article

AN - SCOPUS:85109162957

VL - 109

SP - 551

EP - 562

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 3-4

ER -

ID: 78925776