The properties of solutions of a class of isoperimetric problems of stability optimization (Q1359877)

The differential equation \(y''(x)+\lambda h^{-p}(x)y(x)=0\), \(0<x<1\), with selfadjoint boundary conditions is considered, where \(h\) varies in a certain class \(Q_p\) of nonnegative functions and \(p\) is a nonzero real number. It is investigated whether the first (simple) eigenvalue of this problem has a local or global extremum in the class \(Q_p\).