Resonant periodic solutions in regularized impact oscillator

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Resonant periodic solutions in regularized impact oscillator
 
Makarenkov, Oleg; Verhulst, Ferdinand
(2021) Journal of Mathematical Analysis and Applications, volume 499, issue 2, pp. 1 - 17
(Article)
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.
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Keywords: Asymptotic stability, Impact oscillator, Perturbation theory, Regularization, Resonant periodic solution, Taverne, Analysis, Applied Mathematics
DOI: https://doi.org/10.1016/j.jmaa.2021.125035
ISSN: 0022-247X
Publisher: Academic Press Inc.
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.
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