top
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.
Massimiliano Berti. "Nonlinear vibrations of completely resonant wave equations." Banach Center Publications 77.1 (2007): 49-60. <http://eudml.org/doc/281725>.
@article{MassimilianoBerti2007, abstract = {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.}, author = {Massimiliano Berti}, journal = {Banach Center Publications}, keywords = {quasi-periodic solutions; resonant problems; Dirichlet boundary conditions; small divisors; inifinite-dimensional bifurcations; Nash-Moser implicit function theorems}, language = {eng}, number = {1}, pages = {49-60}, title = {Nonlinear vibrations of completely resonant wave equations}, url = {http://eudml.org/doc/281725}, volume = {77}, year = {2007}, }
TY - JOUR AU - Massimiliano Berti TI - Nonlinear vibrations of completely resonant wave equations JO - Banach Center Publications PY - 2007 VL - 77 IS - 1 SP - 49 EP - 60 AB - 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. LA - eng KW - quasi-periodic solutions; resonant problems; Dirichlet boundary conditions; small divisors; inifinite-dimensional bifurcations; Nash-Moser implicit function theorems UR - http://eudml.org/doc/281725 ER -