A Matching Technique and Structure Theorems for Sturm-liouville Boundary Value Problems with Interior Singularities

Abstract

Asymptotic solutions for the interior double pole Sturm-Liouville boundary value problem are obtained using a method of matched asymptotic approximations. Employing asymptotic forms of the Whittaker functions, the WKB approximations and Airy functions, solutions are obtained valid and non-vanishing on the whole interval. Eigenvalue and eigenfunction theorems are then presented for a generalized parameter-dependent Sturm-Liouville eigenproblem.