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 [P. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math. 20 (1967) 145–205].

Forced vibrations of wave equations with non-monotone nonlinearities

BERTI, MASSIMILIANO;
2006

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 [P. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math. 20 (1967) 145–205].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/100682
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