Open AccessPeriodic solutions of forced Kirchhoff equations
Author(s) -
Pietro Baldi
Publication year - 2009
Publication title -
annali della scuola normale superiore di pisa. classe di scienze
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.444
H-Index - 37
eISSN - 2036-2145
pISSN - 0391-173X
DOI - 10.2422/2036-2145.2009.1.06
Subject(s) - mathematics , uniqueness , mathematical analysis , forcing (mathematics) , periodic boundary conditions , dirichlet boundary condition , dimension (graph theory) , space (punctuation) , boundary value problem , pure mathematics , linguistics , philosophy
We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period 2π/ω and amplitude ∈. We treat both Dirichlet and space-periodic boundary conditions, and both analytic and Sobolev regularity. We prove the existence, regularity and local uniqueness of time-periodic solutions, using a Nash-Moser iteration scheme. The results hold for parameters (ω, ∈) in a Cantor set with asymptotically full measure as ∈ → 0