Magistrelli, Elisa (2011) KAM Theory for PDEs. [Tesi di dottorato] (Unpublished)

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Item Type: Tesi di dottorato
Uncontrolled Keywords: KAM, PDE, resonant, degenerate
Date Deposited: 07 Dec 2011 14:25
Last Modified: 30 Apr 2014 19:49
URI: http://www.fedoa.unina.it/id/eprint/8986

Abstract

This thesis is concerned with KAM theory for Hamiltonian partial differential equations. This theory answers to the following matter: since the solutions of a linear equation are periodic, quasi periodic or almost periodic (for they are superpositions of periodic motions), the problem is to investigate what happens when we add a (sufficiently) small nonlinearity. This thesis contains two new results: an abstract KAM theorem for degenerate infinite--dimensional systems, with an application to the nonlinear wave equation, and a KAM theorem for a completely resonant nonlinear Schr\"odinger equation.

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