  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 $\alpha a$ with bounded $a$ taking on
negative values on a set of positive measure, then there will always exist
unbounded solutions for sufficiently large positive $\alpha$.
  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.
