Small amplitude periodic solutions of Klein–Gordon equations

Lu, Nan

doi:10.1016/j.anihpc.2016.10.002

Lu, Nan

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1255-1272.

Résumé

We consider a class of nonlinear Klein–Gordon equations $u_{t t} = u_{x x} - u + f (u)$ 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.

MR Zbl

DOI : 10.1016/j.anihpc.2016.10.002

Mots clés : Klein–Gordon equation, Periodic solution, Nash–Moser iteration

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     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},
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     year = {2017},
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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. http://www.numdam.org/articles/10.1016/j.anihpc.2016.10.002/

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