It is well known that eigenvalues can be seriously changed by small perturbations of the parameters in the initial problem. We consider a well-posed eigenvalue problem, depending on a continuous function as parameter. This problem originates in some studies concerning the optimization of the ow displacements in porous media (or some analogue models). We approximate the continuous function by a simple (step) function. The eigenvalue problem for the simple function has no solution. As a consequence, we show that the multi-layer method introduced in [1] (in order to minimize the Sa man-Taylor instability) makes no sense. In [2]-[3] we proved that perturbations of some parameters in similar problems can give unbounded eigenvalues for large wavenumbers.