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Morse index of approximating periodic solutions for the billiard problem. Application to existence results |
Canad. J. Math. 50(1998), 497-524
Published:1998-06-01
Printed: Jun 1998
Printed: Jun 1998
- Philippe Bolle
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 |