TY - JOUR
T1 - Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential
JF - Journal of the European Mathematical Society
Y1 - 2013
A1 - Massimiliano Berti
A1 - Philippe Bolle
AB - We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on Td , d ≥ 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C∞ then the solutions are C∞. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. © European Mathematical Society 2013.
VL - 15
N1 - cited By (since 1996)5
ER -
TY - JOUR
T1 - Quasi-periodic solutions of completely resonant forced wave equations
JF - Comm. Partial Differential Equations 31 (2006) 959 - 985
Y1 - 2006
A1 - Massimiliano Berti
A1 - Michela Procesi
AB - We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.
UR - http://hdl.handle.net/1963/2234
U1 - 2010
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Quasi-periodic oscillations for wave equations under periodic forcing
JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116
Y1 - 2005
A1 - Massimiliano Berti
A1 - Michela Procesi
PB - Accademia Nazionale dei Lincei
UR - http://hdl.handle.net/1963/4583
U1 - 4350
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -