N-cyclic functions and multiple subharmonic solutions of Duffing's equation

Sana Gasmi (1) , Alain Haraux (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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’ = εƒ(t) where c and ε are some positive constants and ƒ is, for instance, a sinusoidal function.

Mots clés: second order equation; periodic solution; subharmonic

Domaines: Analyse numérique [math.NA]

Sana Gasmi, Alain Haraux. N-cyclic functions and multiple subharmonic solutions of Duffing's equation. 2007. ⟨hal-00171971⟩