@article {2013,
	title = {A note on KAM theory for quasi-linear and fully nonlinear forced KdV},
	journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437{\textendash}450},
	year = {2013},
	publisher = {European Mathematical Society},
	abstract = {We present the recent results in [3] concerning quasi-periodic solutions
for quasi-linear and fully nonlinear forced perturbations of KdV equations.
For Hamiltonian or reversible nonlinearities the solutions are linearly stable.
The proofs are based on a combination of di erent ideas and techniques:
(i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization
procedure, which conjugates the linearized operator to a di erential operator
with constant coe cients plus a bounded remainder. These transformations
are obtained by changes of variables induced by di eomorphisms of the torus
and pseudo-di erential operators. (iii) A reducibility KAM scheme, which
completes the reduction to constant coe cients of the linearized operator,
providing a sharp asymptotic expansion of the perturbed eigenvalues.},
	keywords = {KAM for PDEs},
	doi = {10.4171/RLM/660},
	author = {P Baldi and Massimiliano Berti and Riccardo Montalto}
}
@article {2011,
	title = {Nonlinear wave and Schr{\"o}dinger equations on compact Lie groups and homogeneous spaces},
	journal = {Duke Mathematical Journal},
	volume = {159},
	year = {2011},
	month = {2011},
	chapter = {479},
	abstract = {We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr{\textasciidieresis}odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.},
	issn = {0012-7094},
	doi = {10.1215/00127094-1433403},
	author = {Massimiliano Berti and Michela Procesi}
}
@article {2001,
	title = {Non-compactness and multiplicity results for the Yamabe problem on Sn},
	journal = {J. Funct. Anal. 180 (2001) 210-241},
	number = {SISSA;130/99/M},
	year = {2001},
	publisher = {Elsevier},
	doi = {10.1006/jfan.2000.3699},
	url = {http://hdl.handle.net/1963/1345},
	author = {Massimiliano Berti and Andrea Malchiodi}
}
