Periodic solutions of wave equations for asymptotically full measure sets of frequencies
Abstract
We prove existence and multiplicity of small amplitude periodic solutions of the completely resonant wave equation utt - uxx + f(x,u)=0 with Dirichlet boundary conditions where f(x,u)=a2 u2 + a3(x) u3 + O(u4) or f(x,u)= a4 u4 + O(u5) for a Cantor-like set of frequencies omega of asymptotically full measure at omega=1.
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