Nonlinear vibrations of completely resonant wave equations
Volume 77 / 2007
Banach Center Publications 77 (2007), 49-60
MSC: 35L05, 37K50, 58E05.
DOI: 10.4064/bc77-0-4
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.
