## Abstract The left‐definiteness for both regular and singular Sturm–Liouville problems is characterized. We give a necessary and sufficient condition on the coefficients, the endpoints and the boundary conditions of Sturm–Liouville problems to determine the left‐definiteness. (© 2005 WILEY‐VCH Ve
Left-Definite Sturm–Liouville Problems
✍ Scribed by Q. Kong; H. Wu; A. Zettl
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 238 KB
- Volume
- 177
- Category
- Article
- ISSN
- 0022-0396
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📜 SIMILAR VOLUMES
## Abstract Various notions of indices for definite and indefinite Sturm‐Liouville problems are introduced and relations between them are investigated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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
For every positive integer n, we construct a class of regular self-adjoint and nonself-adjoint Sturm-Liouville problems with exactly n eigenvalues. These n eigenvalues can be located anywhere in the complex plane in the non-self-adjoint case and anywhere along the real line in the self-adjoint case.
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