83 research outputs found
On Discontinuous Dirac Operator with Eigenparameter Dependent Boundary and Two Transmission Conditions
In this paper, we consider a discontinuous Dirac operator with eigenparameter
dependent both boundary and two transmission conditions. We introduce a
suitable Hilbert space formulation and get some properties of eigenvalues and
eigenfunctions. Then, we investigate Green's function, resolvent operator and
some uniqueness theorems by using Weyl function and some spectral data
Darboux transformations on Sturm-Liouville Eigenvalue Problems with Eigenparameter Dependent Transmission Conditions
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, 2017Sturm-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.XL201
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