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

Open Access article
 Printed: Jun 1998
  • Philippe Bolle
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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, 58E50 show english descriptions Periodic solutions
34C25 - Periodic solutions
58E50 - Applications

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