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# Morse index of approximating periodic solutions for the billiard problem. Application to existence results

Published:1998-06-01
Printed: Jun 1998
• Philippe Bolle
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## Abstract

This paper deals with periodic solutions for the billiard problem in a bounded open set of $\hbox{\Bbbvii R}^N$ 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.
 MSC Classifications: 34C25 - Periodic solutions 58E50 - Applications