- 06-160 Massimiliano Berti, Philippe Bolle
- Cantor families of periodic solutions for wave equations via a variational principle.
May 15, 06
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Abstract. We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of
asymptotically full measure, for new generic sets of nonlinearities, via
a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation -- variational in nature -- defined just on a Cantor-like set because of the presence of
"small divisors". We develop suitable variational tools to deal with this situation and, in particular, we don't require the existence of any non-degenerate solution for the "0th order bifurcation equation" as in previous works.