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

Abstract

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. © 2001 Academic Press.