On the Spectrum of Regular Weighted Sturm-Liouville Problems in the Set of Integers
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Date
2021-01-21
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Addis Ababa University
Abstract
In this thesis, certain in_nite subsets of the set of positive integers are inves-
tigated as possible spectra of regular weighted Sturm-Liouville eigenvalue
problem with separated homogeneous boundary conditions. With the (con-
ditional) exception of the set of square integers, it is shown that all the sets
considered herein are not spectra of such a problem. We also state three
necessary conditions in order for a set to be a spectrum of such eigenvalue
problems. Concepts adopted from the area of study in Mathematical anal-
ysis known as Asymptotic analysis will _gure prominently in the proofs of
the main results.
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Keywords
Spectrum, Regular Weighted, Sturm-Liouville Problems, Set of Integers