Resonant periodic solutions in regularized impact oscillator

Oleg Makarenkov; Ferdinand Verhulst

doi:10.1016/j.jmaa.2021.125035

Resonant periodic solutions in regularized impact oscillator

Oleg Makarenkov^*, Ferdinand Verhulst

^*Corresponding author for this work

University of Texas at Dallas

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

Abstract

We use a perturbation approach to prove the occurrence of asymptotically stable periodic solutions in a bilinear oscillator whose one spring has nearly infinite stiffness. This leads to a singularly perturbed problem where the classical theory does not apply.

Original language	English
Article number	125035
Pages (from-to)	1-17
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	499
Issue number	2
Early online date	2021
DOIs	https://doi.org/10.1016/j.jmaa.2021.125035
Publication status	Published - 15 Jul 2021

Bibliographical note

Funding Information:
The authors are grateful to anonymous Reviewers and the Associate Editor, whose comments helped to improve the paper. The main part of this paper has been written while the first author visited the Institute of Mathematics at the University of Utrecht. He expresses his deep gratitude for the excellent working conditions provided by the Institute. The work of the first author is supported by NSF grant CMMI-1916876 .

Funding Information:
The authors are grateful to anonymous Reviewers and the Associate Editor, whose comments helped to improve the paper. The main part of this paper has been written while the first author visited the Institute of Mathematics at the University of Utrecht. He expresses his deep gratitude for the excellent working conditions provided by the Institute. The work of the first author is supported by NSF grant CMMI-1916876.

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

Asymptotic stability
Impact oscillator
Perturbation theory
Regularization
Resonant periodic solution

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10.1016/j.jmaa.2021.125035

1-s2.0-S0022247X21001141-mainFinal published version, 469 KBLicence: Taverne

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title = "Resonant periodic solutions in regularized impact oscillator",

abstract = "We use a perturbation approach to prove the occurrence of asymptotically stable periodic solutions in a bilinear oscillator whose one spring has nearly infinite stiffness. This leads to a singularly perturbed problem where the classical theory does not apply.",

keywords = "Asymptotic stability, Impact oscillator, Perturbation theory, Regularization, Resonant periodic solution",

author = "Oleg Makarenkov and Ferdinand Verhulst",

note = "Funding Information: The authors are grateful to anonymous Reviewers and the Associate Editor, whose comments helped to improve the paper. The main part of this paper has been written while the first author visited the Institute of Mathematics at the University of Utrecht. He expresses his deep gratitude for the excellent working conditions provided by the Institute. The work of the first author is supported by NSF grant CMMI-1916876 . Funding Information: The authors are grateful to anonymous Reviewers and the Associate Editor, whose comments helped to improve the paper. The main part of this paper has been written while the first author visited the Institute of Mathematics at the University of Utrecht. He expresses his deep gratitude for the excellent working conditions provided by the Institute. The work of the first author is supported by NSF grant CMMI-1916876. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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KW - Perturbation theory

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Resonant periodic solutions in regularized impact oscillator

Abstract

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Keywords

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