Small amplitude periodic solutions of Klein–Gordon equations

Nan Lu

doi:10.1016/j.anihpc.2016.10.002

JournalsaihpcVol. 34, No. 5pp. 1255–1272

Small amplitude periodic solutions of Klein–Gordon equations

Nan Lu
Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL 36849, United States

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Abstract

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

Cite this article

Nan Lu, Small amplitude periodic solutions of Klein–Gordon equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 5, pp. 1255–1272

DOI 10.1016/J.ANIHPC.2016.10.002