Original Articles

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

Published in: Quaestiones Mathematicae
Volume 25 , issue 3 , 2002 , pages: 275–287

DOI: 10.2989/16073600209486015

Author(s): ThomasM. Acho

Keywords: ASYMPTOTIC APPROXIMATION , INTERIOR SINGULARITIES , TURNING POINTS , WHITTAKER , FUNCTIONS , WKB APPROXIMATIONS , AIRY FUNCTIONS , EIGENFUNCTION SOLUTIONS , EIGENVALUE RELATIONS , STOKES PHENOMENA , OUTER EXPANSIONS , INNER EXPANSIONS , HIGHER ORDER MODES , ORDER MODES

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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.

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