Abstract
In order to apply the machinery of critical point theory to study the periodic solutions of Tonelli Lagrangian systems on a closed manifold M, one needs to find a nice functional setting for the Lagrangian action: a suitable free loop space on M with a manifold structure, over which the action is regular, say at least C1, and such that its sublevels satisfy some sort of compactness, such as the Palais-Smale condition.
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© 2012 Springer Basel AG
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Mazzucchelli, M. (2012). Functional Setting for the Lagrangian Action. In: Critical Point Theory for Lagrangian Systems. Progress in Mathematics, vol 293. Springer, Basel. https://doi.org/10.1007/978-3-0348-0163-8_3
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DOI: https://doi.org/10.1007/978-3-0348-0163-8_3
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0162-1
Online ISBN: 978-3-0348-0163-8
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