Abstract
We investigate a bifurcation phenomenon for the periodic solutions of the Duffing equation without damping terms:
d2u/dt2(t) + κ u(t) + αu3(t) = fλ(t), t ∈ R (1.1)
where κ and α are positive constants and fλ(t) (λ > 0) is a given family of T-periodic external force parameterized by λ. We show an existence of not only T and exact 2T-periodic solutions but also exact mT-periodic solutions (m ≥ 3) bifurcated from a specific T-periodic solution.
