Infinity of subharmonics for asymmetric Duffing equations with the Lazer-Leach-Dancer condition (Q5937325)

The existence of infinitely many subharmonics is established to the asymmetric Duffing equation \(x''+g(x)= p(t)\), where \(p(t)\) is a continuous \(2\pi\)-periodic function. The result is proved using a generalized version of the Poincaré-Birkhoff twist theorem by Franks. As a consequence of this result, a sufficient and necessary condition for the existence of arbitrarily large amplitude periodic solutions to a class of asymmetric Duffing equations at resonance is obtained.