We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-4,
author = {Massimiliano Berti},
title = {Nonlinear vibrations of completely resonant wave equations},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {49-60},
zbl = {1121.35083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-4}
}
Massimiliano Berti. Nonlinear vibrations of completely resonant wave equations. Banach Center Publications, Tome 75 (2007) pp. 49-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-4/