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 non-monotone forcing terms / Berti, Massimiliano; Biasco, Luca. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 16:2(2005), pp. 117-124.
Periodic solutions of nonlinear wave equations with non-monotone forcing terms
Berti, Massimiliano;
2005-01-01
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.| File | Dimensione | Formato | |
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