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Morse Index of Approximating Periodic Solutions for the Billiard Problem. Application to Existence Results
Published online by Cambridge University Press: 20 November 2018
Abstract
This paper deals with periodic solutions for the billiard problem in a bounded open set of ${{\mathbb{R}}^{N}}$ which are limits of regular solutions of Lagrangian systems with a potential well. We give a precise link between the Morse index of approximate solutions (regarded as critical points of Lagrangian functionals) and the properties of the bounce trajectory to which they converge.
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- Copyright © Canadian Mathematical Society 1998