Forced vibrations of wave equations with non-monotone nonlinearities
Analysis of PDEs
2007-05-23 v1
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
Cite
@article{arxiv.math/0410619,
title = {Forced vibrations of wave equations with non-monotone nonlinearities},
author = {M. Berti and L. Biasco},
journal= {arXiv preprint arXiv:math/0410619},
year = {2007}
}