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;
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/100681
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