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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.
Mathematics Subject
Classification (2000):
Primary 34B24, 34L20, 34E20; Secondary 33C10, 33C15, 34E05
Quaestiones Mathematicae 25 (2002), 275-287
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.
Mathematics Subject
Classification (2000):
Primary 34B24, 34L20, 34E20; Secondary 33C10, 33C15, 34E05
Quaestiones Mathematicae 25 (2002), 275-287
