次线性非对称Duffing方程的不变环面

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次线性非对称Duffing方程的不变环面张新丽¹, 朴大雄²1. 青岛科技大学数理学院青岛 266061;
2. 中国海洋大学数学科学学院青岛 266100 Invariant Tori of Sublinear Asymmetric Duffing Equations Xin Li ZHANG¹, Da Xiong PIAO²1. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, P. R. China;
2. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P. R. China

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摘要利用Moser扭转定理，在一定的光滑性条件下，证明了次线性非对称Duffing方程x"+a（x+）1/3-b（x^-）1/3+φ（x）=p（t）无穷多不变环面的存在性，从而得到拉格朗日稳定性，其中扰动项φ（x）有界，而强迫项p（t）是周期函数.

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收稿日期: 2020-08-27

MR (2010):

O175.1

基金资助:国家自然科学基金资助项目（11571327，11971059）

通讯作者:朴大雄,E-mail:dxpiao@ouc.edu.cnE-mail: dxpiao@ouc.edu.cn

作者简介: 张新丽,E-mail:zxl@qust.edu.cn

引用本文:

张新丽, 朴大雄. 次线性非对称Duffing方程的不变环面[J]. 数学学报, 2021, 64(6): 967-978. Xin Li ZHANG, Da Xiong PIAO. Invariant Tori of Sublinear Asymmetric Duffing Equations. Acta Mathematica Sinica, Chinese Series, 2021, 64(6): 967-978.

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