ETD Collection

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Author: search.filters.author.Phalafala, Rakgwahla, Jessica

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    Darboux transformations on Sturm-Liouville eigenvalue problems with eigenparameter dependant transmission conditions
    (2017) Phalafala, Rakgwahla, Jessica
    Sturm-Liouville eigenvalue problems arise prominently in mathematical physics. An innumerous amount of complexities have been encountered in solving these problems and a myriad of techniques have been explored over the century. In this work, we investigate one such technique, namely the Darboux-Crum trans formation. This transformation transforms an existing problem into one that is readily solvable or displays properties that are better understood. In particular, we focus our attention on the e↵ect the Darboux-Crum transformation has on the eigenparameter dependence of the transmission condition of our Sturm-Liouville eigenvalue problem.