A Prüfer angle approach to singular Sturm-Liouville problems with Molčanov potentials

Paul Binding; Lyonell Boulton; Patrick J. Browne

doi:10.1016/j.cam.2006.10.032

A Prüfer angle approach to singular Sturm-Liouville problems with Molčanov potentials

Paul Binding, Lyonell Boulton, Patrick J. Browne

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Singular Sturm-Liouville problems for - y^? + qy = ? y on (0, 8) are studied for potentials q which are bounded below and satisfy Molcanov's necessary and sufficient condition for discrete spectrum. A Prüfer angle approach is given for eigenvalue location and eigenfunction oscillation, paralleling that for the regular case. In particular, the eigenvalues are characterized by a "right-hand boundary condition" even though q is of limit point type. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	226-234
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	208
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.cam.2006.10.032
Publication status	Published - 1 Nov 2007

Keywords

Molčanov potential
Prüfer angle
Singular Sturm-Liouville problem

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10.1016/j.cam.2006.10.032

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abstract = "Singular Sturm-Liouville problems for - y? + qy = ? y on (0, 8) are studied for potentials q which are bounded below and satisfy Molcanov's necessary and sufficient condition for discrete spectrum. A Pr{\"u}fer angle approach is given for eigenvalue location and eigenfunction oscillation, paralleling that for the regular case. In particular, the eigenvalues are characterized by a {"}right-hand boundary condition{"} even though q is of limit point type. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

keywords = "Mol{\v c}anov potential, Pr{\"u}fer angle, Singular Sturm-Liouville problem",

author = "Paul Binding and Lyonell Boulton and Browne, {Patrick J.}",

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AU - Boulton, Lyonell

AU - Browne, Patrick J.

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Y1 - 2007/11/1

N2 - Singular Sturm-Liouville problems for - y? + qy = ? y on (0, 8) are studied for potentials q which are bounded below and satisfy Molcanov's necessary and sufficient condition for discrete spectrum. A Prüfer angle approach is given for eigenvalue location and eigenfunction oscillation, paralleling that for the regular case. In particular, the eigenvalues are characterized by a "right-hand boundary condition" even though q is of limit point type. © 2006 Elsevier B.V. All rights reserved.

AB - Singular Sturm-Liouville problems for - y? + qy = ? y on (0, 8) are studied for potentials q which are bounded below and satisfy Molcanov's necessary and sufficient condition for discrete spectrum. A Prüfer angle approach is given for eigenvalue location and eigenfunction oscillation, paralleling that for the regular case. In particular, the eigenvalues are characterized by a "right-hand boundary condition" even though q is of limit point type. © 2006 Elsevier B.V. All rights reserved.

KW - Molčanov potential

KW - Prüfer angle

KW - Singular Sturm-Liouville problem

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U2 - 10.1016/j.cam.2006.10.032

DO - 10.1016/j.cam.2006.10.032

M3 - Article

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EP - 234

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1 SPEC. ISS.

ER -

A Prüfer angle approach to singular Sturm-Liouville problems with Molčanov potentials

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Keywords

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