We prove existence and multiplicity of small amplitude periodic solutions with large period for the wave equation with small "mass". Such solutions bifurcate from resonant finite-dimensional invariant tori of the fourth order Birkhoff normal form of the associated hamiltonian system. The number of geometrically distinct solutions and their minimal periods tend to infinity when the "mass" tends to zero.
Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation / Biasco, L.; Di Gregorio, L.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 17:1(2006), pp. 25-33. [10.4171/RLM/452]
Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation
Di Gregorio L.
2006
Abstract
We prove existence and multiplicity of small amplitude periodic solutions with large period for the wave equation with small "mass". Such solutions bifurcate from resonant finite-dimensional invariant tori of the fourth order Birkhoff normal form of the associated hamiltonian system. The number of geometrically distinct solutions and their minimal periods tend to infinity when the "mass" tends to zero.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
