We present new existence and regularity results 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. 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 Rabinowitz.
Periodic solutions of nonlinear wave equations with nonmonotone forcing terms / Berti, Massimiliano; L., Biasco. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. CLASSE DI SCIENZE FISICHE, MATEMATICHE E NATURALI. RENDICONTI LINCEI. SUPPLEMENTO. - ISSN 1121-3094. - STAMPA. - 16:2(2005), pp. 107-124.
Periodic solutions of nonlinear wave equations with nonmonotone forcing terms
BERTI, MASSIMILIANO;
2005
Abstract
We present new existence and regularity results 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. 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 Rabinowitz.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
