Darboux transformations on Sturm-Liouville Eigenvalue Problems with Eigenparameter Dependent Transmission Conditions

• Main Author: Rakgwahla, Jessica
• Format: Others
• Language: en
• Published: 2018
• Online Access: https://hdl.handle.net/10539/24838

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg. In fulfillment of the requirements for the degree of Master of Science, 2017 === 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. === XL2018