@article {Berti20122579,
title = {Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential},
journal = {Nonlinearity},
volume = {25},
number = {9},
year = {2012},
note = {cited By (since 1996)3},
pages = {2579-2613},
abstract = {We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d >= 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the {\textquoteright}separation properties{\textquoteright} of the small divisors assuming weaker non-resonance conditions than in [11]. {\textcopyright} 2012 IOP Publishing Ltd.},
issn = {09517715},
doi = {10.1088/0951-7715/25/9/2579},
author = {Massimiliano Berti and Philippe Bolle}
}