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 related to the regularity theory of [18].
Berti, M., Biasco, L. (2006). Forced vibrations of wave equations with non-monotone nonlinearities. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE.
Forced vibrations of wave equations with non-monotone nonlinearities
BIASCO, LUCA
2006-01-01
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 related to the regularity theory of [18].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.