On The Spectrum Of Regular Weighted Sturm-liouville Problems In The Set Of Integers

In this thesis, certain in_nite subsets of the set of positive integers are inves-rntigated as possible spectra of regular weighted Sturm-Liouville eigenvaluernproblem with separated homogeneous boundary conditions. With the (con-rnditional) exception of the set of square integers, it is shown that all the setsrnconsidered herein are not spectra of such a problem. We also state threernnecessary conditions in order for a set to be a spectrum of such eigenvaluernproblems. Concepts adopted from the area of study in Mathematical anal-rnysis known as Asymptotic analysis will _gure prominently in the proofs ofrnthe main results.

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