Forced vibrations of wave equations with non-monotone nonlinearities

2004/10/29 by M. Berti, Berti, M., L. Biasco +1
Mathematics · #35B10 #35L05 #35L20 #37K10 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B10 #msc:35L05 #msc:35L20 #msc:37K10

paper · pdf · doi:10.48550/arxiv.math/0410619

arxiv created 2004/10/29 · arxiv updated 2009/12/01

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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