where lambda and alpha(i), beta(i) are spectral and physical parameters, respectively, and p(x), q(x), r(x) are positive and regular functions in [0, L]. Our survey is focused mainly on the case alpha(1) > 0 and beta(1) < 0, where neither self-adjoint operator theorems on Hilbert spaces nor Sturm's comparison results can be used directly. We describe the spectrum and the oscillatory results of the eigenfunctions from a geometrical approach, using a function related to the Prufer angle. The proofs of the asymptotic results of the eigenvalues and separation theorem of the eigenfunctions are developed through classical second-order differential equation tools. Finally, the results on the spectrum of (0.1) are used to study the linear stability of three-layer Hele-Shaw flows, which is a simple model for the fingering phenomenon on the flooding oil recovery process.