Unstable even-parity eigenmodes of the regular static SU(2) Yang-Mills-dilaton solutions

In this paper we obtain unstable even-parity eigenmodes to the static regular spherically symmetric solutions of the SU(2) Yang-Mills-dilaton coupled system of equations in 3+1 Minkowski space-time. The corresponding matrix Sturm-Liouville problem is solved numerically by means of the continuous analogue of Newton's method. The method, being the powerful tool for solving both boundary-value and Sturm-Liouville problems, is described in details.