  We study the stability of 5D gravitational solutions containing an arbitrary
number of scalar fields. A closed set of equations is derived which governs the
background and perturbations of N scalar fields and the metric, for arbitrary
bulk and boundary scalar potentials. In particular the effect of the
energy-momentum tensor of the scalar fields on the geometry is fully taken into
account, together with all the perturbations of the system. The equations are
explicitly written as an eigenvalue problem, which can be readily solved to
determine the stability of the system and obtain the properties of the
fluctuations, such as masses and couplings. As an example, we study a dynamical
soft-wall model with two bulk scalar fields used to model the hadron spectrum
of QCD and the Higgs sector of electroweak physics. It is shown that there are
no tachyonic modes, and that there is a (radion) mode whose mass is suppressed
by a large logarithm compared to that of the other Kaluza-Klein modes.
