Solutions anti-périodiques multiples de x'' + cx' + g(x) = εf(t)

Sana Gasmi (1)

1 LJLL - Laboratoire Jacques-Louis Lions

Following a work of P. Souplet which presents an example showing the nonuniqueness of antiperiodic solutions of a second order ordinary equation, we show, using a method of W.S. Loud the existence of 4 antiperiodic solutions of the equation x'' + cx' + αx + βx³ = εf(t) for a function f. Then we give concrete conditions for the existence of 3 or 4 periodic solutions of the same equation. In both cases f can be chosen analytic.

Domaines: Analyse numérique [math.NA]

Sana Gasmi. Solutions anti-périodiques multiples de x'' + cx' + g(x) = εf(t). 2007. ⟨hal-00153505⟩