We consider a Sturm -Liouville operator Lu = -(r(t)u ) +p(t)u, where r is a (strictly) positive continuous function on ]a, b[ and p is locally integrable on ]a, b[ . Let r 1 (t) = t a (1/r) ds and choose any c ∈ ]a, b[ . We are interested in the eigenvalue problem Lu = λm(t)u, u(a) = u(b) = 0, and t
Singular Sturm–Liouville Theory on Manifolds
✍ Scribed by Rafe Mazzeo; Robert McOwen
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 370 KB
- Volume
- 176
- Category
- Article
- ISSN
- 0022-0396
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## Abstract Singular boundary conditions are formulated for non‐selfadjoint Sturm–Liouville problems which are limitcircle in a very general sense. The characteristic determinant is constructed and it is shown that it can be used to extend the Birkhoff theory for so called “Birkhoff regular boundar
We develop a simple oscillation theory for singular Sturm -Liouville problems and combine it with recent asymptotic results, and with the AWA interval-arithmetic code for integration of initial value problems with guaranteed error bounds, to obtain eigenvalue approximations with guaranteed error bou