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

AbstractIn 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

Modulated amplitude waves with nonzero phases in Bose-Einstein condensates

In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using aver- aging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and we also study the stability and instability of modulated amplitude waves (periodic or quasi-periodic). Compared with the previous work, modulated amplitude waves studied in this paper have nontrivial phases and this makes the problem become more diffcult, since it involves some singularities.Comment: 17 pages, 2 figure