An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation

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.

26 pages

References in corpus (2)

• Reducible quasi-periodic solutions for the Non Linear Schrödinger equation
• KAM for the Klein Gordon equation on ${\mathbb{S}}^d$