In this paper we consider the completely resonant beam equation on \T^2 with cubic nonlinearity on a subspace of L^2 (\T^2) which will be explained later. We establish an abstract… Click to show full abstract
In this paper we consider the completely resonant beam equation on \T^2 with cubic nonlinearity on a subspace of L^2 (\T^2) which will be explained later. We establish an abstract infinite dimensional KAM theorem and apply it to the completely resonant beam equation. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional tori.
Keywords:
beam equation;
infinite dimensional;
completely resonant;
resonant beam
Journal Title: Journal of Mathematical Physics
Year Published: 2018
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Journal Title: Journal of Mathematical Physics
Year Published: 2018
Link to full text (if available)
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recommendations!