  In this paper we show that problem of proving the existence of a countable
number of solutions to the static spherically symmetric SU(2)
Einstein-Yang-Mills-dilaton (EYMd) equations can be reduced to proving the
non-existence of solutions to the linearized Yang-Mills-dilaton equations
(lYMd) satisfying certain asymptotic conditions. The reduction from a
non-linear to a linear problem is achieved using a Newtonian perturbation type
argument.
