  We take advantage of the Sturm-Liouville eigenvalue problem to analytically
study the holographic insulator/superconductor phase transition in the probe
limit. The interesting point is that this analytical method can not only
estimate the most stable mode of the phase transition, but also the second
stable mode. We find that this analytical method perfectly matches with other
numerical methods, such as the shooting method. Besides, we argue that only
Dirichlet boundary condition of the trial function is enough under certain
circumstances, which will lead to a more precise estimation. This relaxation
for the boundary condition of the trial function is first observed in this
paper as far as we know.
