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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ltu-18326 |
| Date | January 2014 |
| Creators | Kikonko, Mervis |
| Publisher | Luleå tekniska universitet, Matematiska vetenskaper |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Licentiate thesis / Luleå University of Technology, 1402-1757 |
Page generated in 0.0013 seconds