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On a Non-Analytic Perturbation Problem

Published online by Cambridge University Press:  20 November 2018

C. A. Swanson
C. A. Swanson*
Affiliation:
University of British Columbia
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The purpose here is to study a type of perturbation problem, arising from a differential equation, which is not included in the realm of analytic or asymptotic perturbation theory [4], [6]. Such a problem arises when the domain of the differential operator has been subjected to a variation (rather than the formal operator). We propose to outline one simple problem of this type, concerned with a second order ordinary differential operator. Our purpose is to obtain asymptotic estimates for the characteristic values of a regular Sturm-Liouville problem on a closed interval [a, b] when b is near a singular point of the differential operator. Similar results have been obtained in [3], [8], and [9] by other methods.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 3 , September 1961 , pp. 243 - 248
Copyright
Copyright © Canadian Mathematical Society 1961

References

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