半线性Klein-Gordon方程的高频周期解

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 484-500.

半线性Klein-Gordon方程的高频周期解

童常青¹,郑静^2,*()

¹ 杭州电子科技大学理学院数学系杭州 310018
² 杭州电子科技大学经济学院统计系杭州 310018

收稿日期:2017-01-09 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 郑静 E-mail:tongchangqing@hdu.edu.cn
基金资助:
国家社科基金(17BTJ023)

Periodic Solutions of a Semi-Linear Klein-Gordon Equations with High Frequencies

Changqing Tong¹,Jing Zheng^2,*()

¹ Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou 310018
² Department of Statistics, College of Economy, Hangzhou Dianzi University, Hangzhou 310018

Received:2017-01-09 Online:2019-06-26 Published:2019-06-27
Contact: Jing Zheng E-mail:tongchangqing@hdu.edu.cn
Supported by:
the The National Social Science Fund of China(17BTJ023)

摘要/Abstract

摘要：

该文对一些半线性Klein-Gordon方程，证明了高频周期解的存在性.对非线性项只假设它的正则性为C^k，且没有非线性项非常小的假设.利用Nash-Moser迭代，在Sobolev空间中得到了周期解.

关键词: Klein-Gordon方程, 周期解, Nash-Moser迭代

Abstract:

In this paper, we prove the existence of periodic solutions with high frequencies of some semi-linear Klein-Gordon equations. We only assume the nonlinearities are C^k regular and without smallness. Using Nash-Moser iteration, we obtained some periodic solutions in Sobolev space.

Key words: Klein-Gordon equation, Periodic solutions, Nash-Moser Iteration

中图分类号:

O175.27

童常青,郑静. 半线性Klein-Gordon方程的高频周期解[J]. 数学物理学报, 2019, 39(3): 484-500.

Changqing Tong,Jing Zheng. Periodic Solutions of a Semi-Linear Klein-Gordon Equations with High Frequencies[J]. Acta mathematica scientia,Series A, 2019, 39(3): 484-500.

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