Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 484-500.

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

Changqing Tong1,Jing Zheng2,*()   

  1. 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
  • Supported by:
    the The National Social Science Fund of China(17BTJ023)


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 Ck 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

CLC Number: 

  • O175.27