Forced vibrations of wave equations with non-monotone nonlinearities

M. Berti; L. Biasco

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Forced vibrations of wave equations with non-monotone nonlinearities

M. Berti·L. Biasco

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Abstract

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz

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M. Berti, L. Biasco. 2004-10-29. Forced vibrations of wave equations with non-monotone nonlinearities. https://arxiv.org/abs/math/0410619

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