Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems
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, u...
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Luleå tekniska universitet, Matematiska vetenskaper
2014
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ftluleatu:oai:DiVA.org:ltu-18326 2023-12-17T10:33:14+01:00 Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems Kikonko, Mervis 2014 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18326 eng eng Luleå tekniska universitet, Matematiska vetenskaper Licentiate thesis / Luleå University of Technology, 1402-1757 orcid:0000-0002-8898-4547 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18326 urn:isbn:978-91-7583-093-3 urn:isbn:978-91-7583-094-0 Local 807ad19f-e52c-4e21-9b7c-0088ee9db556 info:eu-repo/semantics/openAccess Mathematical Analysis Matematisk analys Licentiate thesis, comprehensive summary info:eu-repo/semantics/masterThesis text 2014 ftluleatu 2023-11-23T17:10:41Z 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 et.al, 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. 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 ... Master Thesis Luleå Luleå Luleå University of Technology Publications (DiVA) Atkinson ENVELOPE(-85.483,-85.483,-78.650,-78.650) Persson ENVELOPE(-58.400,-58.400,-64.200,-64.200) Sturm ENVELOPE(162.967,162.967,-71.050,-71.050) |
institution |
Open Polar |
collection |
Luleå University of Technology Publications (DiVA) |
op_collection_id |
ftluleatu |
language |
English |
topic |
Mathematical Analysis Matematisk analys |
spellingShingle |
Mathematical Analysis Matematisk analys Kikonko, Mervis Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems |
topic_facet |
Mathematical Analysis Matematisk analys |
description |
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 et.al, 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. 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 ... |
format |
Master Thesis |
author |
Kikonko, Mervis |
author_facet |
Kikonko, Mervis |
author_sort |
Kikonko, Mervis |
title |
Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems |
title_short |
Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems |
title_full |
Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems |
title_fullStr |
Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems |
title_full_unstemmed |
Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems |
title_sort |
qualitative and spectral theory of some regular non-definite sturm-liouville problems |
publisher |
Luleå tekniska universitet, Matematiska vetenskaper |
publishDate |
2014 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18326 |
long_lat |
ENVELOPE(-85.483,-85.483,-78.650,-78.650) ENVELOPE(-58.400,-58.400,-64.200,-64.200) ENVELOPE(162.967,162.967,-71.050,-71.050) |
geographic |
Atkinson Persson Sturm |
geographic_facet |
Atkinson Persson Sturm |
genre |
Luleå Luleå |
genre_facet |
Luleå Luleå |
op_relation |
Licentiate thesis / Luleå University of Technology, 1402-1757 orcid:0000-0002-8898-4547 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18326 urn:isbn:978-91-7583-093-3 urn:isbn:978-91-7583-094-0 Local 807ad19f-e52c-4e21-9b7c-0088ee9db556 |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1785587155033128960 |