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Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this Licentiate thesis, we study some regular non-definite Sturm-Liouville problems. In this case, the weight function takes on both positive and negative signs on a given interval [a, b]. One feature of the non-definite Sturm-Liouville problem is the possible existence of non-real eigenvalues, unlike in the definite case (i.e. left or right definite) in which only real eigenvalues exist.This thesis consists of three papers (papers A-C) and an introduction to this area, which puts these papers into a more general frame.In paper A we give some precise estimates on the Richardson number for the two turning point case, thereby complementing the work of Jabon and Atkinson in an essential way. We also give a corrected version of their result since there seems to be a typographical error in their paper.In paper B we show that the interlacing property which holds in the one turning point case does not hold in the two turning point case. The paper consists of a detailed presentation of numerical results of the case in which the weight function is allowed to change its sign twice in the interval (−1, 2). We also present some theoretical results which support the numerical results.In paper C we extend results found in the paper by Jussi Behrndt, in an essential way, to a case in which the weight function vanishes identically in a subinterval of [a, b]. In particular, we present some surprising numerical results on a specific problem in which the weight function is allowed to vanish identically on a subinterval of [−1, 2]. We also give some theoretical results which support these numerical examples.

Place, publisher, year, edition, pages
Luleå tekniska universitet, 2014.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
Research subject
URN: urn:nbn:se:ltu:diva-18326Local ID: 807ad19f-e52c-4e21-9b7c-0088ee9db556ISBN: 978-91-7583-093-3 (print)ISBN: 978-91-7583-094-0 (electronic)OAI: diva2:991333
Godkänd; 2014; 20141110 (merkok); Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Mervis Kikonko Ämne: Matematik/Mathematics Uppsats: Qualitative and Spectral Theory of Some Regular Non-Definite Sturm-Liouville Problems Examinator: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Professor Sten Kaijser, Matematiska Institutionen, Uppsala Universitet Tid: Fredag den 11 december 2014 kl 10,00 Plats: E243, Luleå tekniska universitetAvailable from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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