86 citations · 197 across the 14 of their papers we have counts for
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Quasi-periodic solutions of nonlinear wave equations on the d-dimensional torus
Massimiliano Berti, Philippe Bolle
The main result of this research Monograph is the existence of small amplitude time quasi-periodic solutions for autonomous nonlinear wave equations $$ u_{tt} - Δu + V(x) u + g(x,…
Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential
Massimiliano Berti, Philippe Bolle
We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodical…
Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential
Massimiliano Berti, Philippe Bolle
We prove the existence of quasi-periodic solutions for Schroedinger equations with a multiplicative potential on T^d, d \geq 1, merely differentiable nonlinearities, and tangential…
Cantor families of periodic solutions for completely resonant nonlinear wave equations
M. Berti, P. Bolle
We prove existence of small amplitude, $2π\slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequen…
Bifurcation of free vibrations for completely resonant wave equations
M. Berti, P. Bolle
We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency o…
Periodic solutions of nonlinear wave equations with general nonlinearities
Massimiliano Berti, Philippe Bolle
We prove the existence of small amplitude periodic solutions, with strongly irrational frequency $ \om $ close to one, for completely resonant nonlinear wave equations. We provide…