中文摘要：

构造了相关的Hamilton函数,用Poincar-éBirkhoff扭转定理证明了具有有界恢复力Duffing方程次调和解的存在性和多重性;并用Massera定理得到调和解的存在性.

英文摘要：

In the paper,we will prove the existence of harmonic solution and infinitely many subharmonic solutions for Duffing equation with bounded restore force：x″＋g（x）=p（t）,where g（x） is a bounded function such that sgn（x）g（x）≥E0〉P0=maxt∈｜p（t）｜ for ｜x｜≥d0,t∈R,besides g（x） satisfies local-Lipschitz condition.