Geodesic
Small amplitude periodic solutions of Klein–Gordon equations
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1255-1272

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We consider a class of nonlinear Klein–Gordon equations utt=uxx−u+f(u) and obtain a family of small amplitude periodic solutions, where the temporal and spatial period have different scales. The proof is based on a combination of Lyapunov–Schmidt reduction, averaging and Nash–Moser iteration.

DOI : 10.1016/j.anihpc.2016.10.002
Keywords: Klein–Gordon equation, Periodic solution, Nash–Moser iteration 
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     author = {Lu, Nan},
     title = {Small amplitude periodic solutions of {Klein{\textendash}Gordon} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1255--1272},
     publisher = {Elsevier},
     volume = {34},
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     year = {2017},
     doi = {10.1016/j.anihpc.2016.10.002},
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     zbl = {1388.35006},
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Lu, Nan. Small amplitude periodic solutions of Klein–Gordon equations. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1255-1272. doi: 10.1016/j.anihpc.2016.10.002

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