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MR1487629 (99m:34107) 34C37 (58E05 58F15)
Montecchiari, Piero; Nolasco, Margherita; Terracini, Susanna A global condition for periodic Duffing-like equations. Trans. Amer. Math. Soc. 351 (1999), no. 9, 3713–3724.
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