Infinity of Subharmonics for Asymmetric Duffing Equations with the Lazer–Leach–Dancer Condition

In this paper, based on a generalized version of the Poincaré–Birkhoff twist theorem by Franks, we establish the existence of infinitely many subharmonics for the asymmetric Duffing equation with the classical Lazer–Leach–Dancer condition. As a consequence of our result, we obtain a sufficient and necessary condition for existence of arbitrarily large amplitude periodic solutions for a class of asymmetric Duffing equations at resonance.