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The existence of at least two homoclinic orbits is proved by A. Ambrosetti and V. Coti Zelati (Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ. Padova, 89 (1993), 177-194) for autonomous Lagrangian systems
Julia Schmale, Roman Pohorsky, Alireza Moallemi
David Andrew Barry, Ulrich Lemmin, Mehrshad Foroughan
Alexis Berne, Etienne Gabriel Henri Vignon, Anne-Claire Marie Billault--Roux, Josué Etienne Gehring, Alfonso Ferrone