Resume
En partant des travaux de F. Clarke et I. Ekeland, on écrit une version en dimension finie de leur principe de dualité (cela est obtenu par une méthode de discrétisation).
De ce résultat on déduit un algorithme qui permet de trouver des solutions périodiques approchées.à des équations différentielles non-linéaires.
On illustre cette méthode par les résultats obtenus pour l’équation :
Abstract
Using the works of F. Clarke and I. Ekeland, one shows a similar dual principle in the finite dimensionnal case, by discretisation.
From this result, we infer an algorithm (which has been computed), to find periodic solutions to non-linear differential equations.
Finally, we illustrate this method by some numerical results concerning the equation :
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Mancini, G. (1983). Periodic Solutions of Hamiltonian Systems Having Prescribed Minimal Period. In: Aubin, J.P., Bensoussan, A., Ekeland, I. (eds) Advances in Hamiltonian Systems. Annals of CEREMADE, vol 2. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6728-4_3
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