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

Pietro Baldi; Massimiliano Berti

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

Pietro Baldi·Massimiliano Berti

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Abstract

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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Pietro Baldi, Massimiliano Berti. 2005-12-02. Periodic solutions of wave equations for asymptotically full measure sets of frequencies. https://arxiv.org/abs/math/0512053

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