Periodic solutions of wave equations for asymptotically full measure sets of frequencies

Baldi, Pietro; Berti, Massimiliano

Periodic solutions of wave equations for asymptotically full measure sets of frequencies

Authors

Description

We prove existence and multiplicity of small amplitude periodic solutions of the completely resonant wave equation u_tt - u_xx + f(x,u)=0 with Dirichlet boundary conditions where f(x,u)=a_2 u^2 + a_3(x) u^3 + O(u^4) or f(x,u)= a_4 u^4 + O(u^5) for a Cantor-like set of frequencies omega of asymptotically full measure at omega=1.
18 pages