Analysis of Sturm-Liouville Eigenproblem with Interior Singularities and a Perturbation Parameter

Abstract

We devote this work to the discussion underpinning the derivation of eigenvalues and eigenfunction solutions for Sturm-Liouville boundary value problems. The study reveals that the parameter dependent nonstandard Sturm-Liouville boundary value problem with interior singularities may have more than two turning points. The Titchmarsh-Weylm-function theory is applied here to obtain eigenfunction solutions valid for the whole interval in which pole singularities and two turning points are present. For the first time, with minimal constraints, the validity of the eigenfunction solutions are discussed when there are more than two turning points present. The eigenvalues are subsequently derived.