Don Hinton, Maeve L. McCarthy, Optimization of the minimum eigenvalue for a class of second order differential operators, UAB Proceedings, to appear.
We consider the problem of how the least eigenvalue of a Sturm-Liouville problem changes as the coefficients are varied. For a certain class of such problems, it is proved that the least eigenvalue can be maximized by placing constraints on the coefficients. Applications are made to various types of column problems. As a preliminary, we develop the spectral theory for a one term operator which has application to a variety of Sturm-Liouville problems.