 04342 M. Berti, P. Bolle
 Cantor families of periodic solutions for completely resonant nonlinear wave equations
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Oct 29, 04

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Abstract. We prove existence of small amplititude $2 \pi/omega$ periodic solutions of
completely resonant nonlinear wave equations with Dirichlet boundary
conditions for any frequency $\omega$ belinging to
a Cantorlike set of positive measure and for a new set
of nonlinearities. The proof relies on a suitable LyapunovSchmidt
decomposition and a variant of the NashMoser Implicit Function Theorem,
In spite of the complete resonance of the equation we show that we can
still reduce the proble to a finite dimensional bifurcation equation.
Moreover, a new simple approach for the inversion of the
linearized operators required by the NashMoser approach is
developed. It allows to deal also
with nonlinearities which are not off and with finite spatial regularity.
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