Location of zeros for Neumann Sturm-Liouville eigenfunctions (Q1827067)

There are many papers concerning the so-called ``Sturm-comparison'' theorems to realize the position and oscillation of zeros of solutions of Sturm-Liouville problems. However, if one tries to realize the position of the zeros of the eigenfunctions of a Sturm-Liouville operator, then the above mentioned results often cannot be used since the eigenvalue, which is a part of the equation, is a priori not known. In this paper, the author gives some results on the zeros and the extremal points of the Neumann Sturm-Liouville eigenfunctions. To this end, the author uses a variational method.