Extrema of functions of eigenvalues

We consider the question of finding an extreme value for some function of the eigenvalues of the differential equation y″ + λφ(x) y = 0,y(0) = y(1) = 0, as φ(x) varies over a region in a function space. A characterization of the φ(x) at which the function of the eigenvalues achieves its extremum is derived. © 1979.