Characterizing degenerate Sturm-Liouville problems
| dc.contributor.author | Mingarelli, Angelo B. | |
| dc.date.accessioned | 2021-05-14T19:21:18Z | |
| dc.date.available | 2021-05-14T19:21:18Z | |
| dc.date.issued | 2004-11-12 | |
| dc.description.abstract | Consider the Dirichlet eigenvalue problem associated with the real two-term weighted Sturm-Liouville equation -(p(x)y')' = λr(x)y on the finite interval [a, b]. This eigenvalue problem will be called degenerate provided its spectrum fills the whole complex plane. Generally, in degenerate cases the coefficients p(x), r(x) must each be sign indefinite on [a, b]. Indeed, except in some special cases, the quadratic forms induced by them on appropriate spaces must also be indefinite. In this note we present a necessary and sufficient condition for this boundary problem to be degenerate. Some extensions are noted. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 8 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Mingarelli, A. B. (2004). Characterizing degenerate Sturm-Liouville problems. <i>Electronic Journal of Differential Equations, 2004</i>(130), pp. 1-8. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13551 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Sturm-Liouville theory | |
| dc.subject | Eigenvalues | |
| dc.subject | Degenerate operators | |
| dc.subject | Spectral theory | |
| dc.subject | Dirichlet problem | |
| dc.title | Characterizing degenerate Sturm-Liouville problems | |
| dc.type | Article |