A Remark on the Qualitative Spectral Theory or Sturm-Liouville Operators

Abstract

If $N(\Lambda )$ denotes the maximal number of zeros of the non-trivial solutions of the Sturm-Liouville equation

then under some hypothesis the number of eigenvalues of a special selfadjoint operator (Friedrichs extension) is equal to $N\Lambda -1$ below $\Lambda$.