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On Periodic Solutions to Constrained Lagrangian System

Part of: Qualitative theory

Published online by Cambridge University Press:  18 December 2019

Oleg Zubelevic
Oleg Zubelevic*
Affiliation:
Dept. of Theoretical mechanics, Mechanics and Mathematics Faculty, M. V. Lomonosov Moscow State University, Russia, 119899, Moscow, MGU
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Abstract

A Lagrangian system is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.

Keywords

Lagrangian systemperiodic solution

MSC classification

Primary: 34C25: Periodic solutions
Secondary: 70F20: Holonomic systems
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 1 , March 2020 , pp. 242 - 255
Copyright
© Canadian Mathematical Society 2019

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Footnotes

Partially supported by grant RFBR 18-01-00887

References

Adams, R. A. and Fournier, J. J. F., Sobolev spaces, Second ed., Pure and Applied Mathematics (Amsterdam), 140, Elsevier, Amsterdam, 2003.Google Scholar
Capozzi, A., Fortunato, D., and Salvatore, A., Periodic solutions of Lagrangian systems with bounded potential. J. Math. Anal. Appl. 124(1987), 482–494.CrossRefGoogle Scholar
Edwards, R., Functional analysis. New York, 1965.Google Scholar
Ekeland, I. and Témam, R., Convex analysis and variational problems. Classics in Applied Mathematics, 28, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999. https://doi.org/10.1137/1.9781611971088CrossRefGoogle Scholar
Kolmogorov, A. and Fomin, S., Elements of the theory of functions and functional analysis. Ukraine, 1999.Google Scholar
Mawhin, J. and Willem, M., Critical point theory and Hamiltonian systems. Springer-Verlag, New York, 1989. https://doi.org/10.1007/978-1-4757-2061-7CrossRefGoogle Scholar
Struwe, M., Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems. Ergebnisse der Mathematik und ihrer Grenzgebiete, 34, Springer-Verlag, Berlin, 2008.Google Scholar