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- W2063203664 abstract "We introduce, in the abstract framework of finite isometry groups on a Hilbert space, a generalization of antiperiodicity called N-cyclicity. The non-existence of N-cyclic solutions of a certain type for the autonomous ODE x″+g(x)=0 implies the existence of N different subharmonic solutions for some forced equations of the type x″+g(x)+cx′=εf(t) where c and ε are some positive constants and f is, for instance, a sinusoidal function. On introduit, dans le cadre général des groupes finis dʼisométries sur un espace de Hilbert réel, une généralisation de lʼanti-périodicité appelée N-cyclicité. Lʼinexistence de solutions N-cycliques dʼun certain type pour lʼéquation autonome x″+g(x)=0 permet de déduire lʼexistence of N solutions sous-harmoniques pour lʼéquation de Duffing forcée avec dissipation x″+g(x)+cx′=εf(t) où c et ε sont des constantes positives et f est par exemple, une fonction sinusoidale." @default.
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- W2063203664 date "2012-05-01" @default.
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- W2063203664 title "N-cyclic functions and multiple subharmonic solutions of Duffingʼs equation" @default.
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- W2063203664 doi "https://doi.org/10.1016/j.matpur.2009.08.005" @default.
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