Open AccessA semilinear wave equation with smooth data and no resonance having no continuous solution
Author(s) -
José F. Caicedo,
Alfonso Castro
Publication year - 2009
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2009.24.653
Subject(s) - monotonic function , resonance (particle physics) , forcing (mathematics) , mathematical analysis , nonlinear system , boundary value problem , wave equation , mathematics , boundary (topology) , physics , particle physics , quantum mechanics
We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.
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