2004/06/02 by Pedro Freitas, David Krejcirik
Mathematics · #math.AP #math.SP #msc:35L20 #msc:35B35 #msc:47A75
published as J. Differential Equations 211 (2005), no. 1, 168-186. · LaTeX, 19 pages; to appear in J. Differential Equations
arxiv created 2004/06/02 · arxiv updated 2009/12/01
We extend some previous results for the damped wave equation in bounded domains in Euclidean spaces to the unbounded case. In particular, we show that if the damping term is of the form αa with bounded a taking on negative values on a set of positive measure, then there will always exist unbounded solutions for sufficiently large positive α. In order to prove these results, we generalize some existing results on the asymptotic behaviour of eigencurves of one-parameter families of Schrodinger operators to the unbounded case, which we believe to be of interest in their own right.