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In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the d-dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of… Click to show full abstract
In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the d-dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of this type for a quasi-linear equation in high dimension. The proof is based on a Nash–Moser scheme in Sobolev class and a regularization procedure combined with a multiscale analysis in order to solve the linearized problem at any approximate solution.
Keywords:
solutions forced;
kirchhoff equation;
periodic solutions;
forced kirchhoff;
equation;
quasi periodic
Journal Title: Nonlinearity
Year Published: 2018
Link to full text (if available)
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Journal Title: Nonlinearity
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!