Spectrum of a regular weighted Sturm-Liouville problem and certain in nite sets of integers

Abstract

Certain infinite subsets of the set of positive integers are investigated as possible spectra of Regular Weighted Sturm-Liouville-Eigenvalue problem with separated homogeneous boundary conditions. With the (conditional) exception of the set of square integers, it is shown that all the sets considered herein are not spectra of such a problem. Concepts adopted from the area of study in Mathematical analysis known as asymptotic analysis will figure prominently in the proofs of the main results