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

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

2005-12-02

arxiv.org/abs/math/0512053v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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.

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