Criteria for Sturm-Liouville equations to have continuous spectra (Q788166)
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scientific article; zbMATH DE number 3842284
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Criteria for Sturm-Liouville equations to have continuous spectra |
scientific article; zbMATH DE number 3842284 |
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Criteria for Sturm-Liouville equations to have continuous spectra (English)
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1983
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The author establishes two sets of sufficient conditions on the locally integrable function q for the equation \(y''+(\lambda -q)y=0\) to have no non-trivial solutions in \(L^ 2[a,\infty)\). In particular the case q(t)\(\to -\infty\) as \(t\to \infty\) is considered. The results are compared with a result of \textit{M. S. P. Eastham} [Nieuw. Arch. Wiskunde, III. Ser. 25, 169-181 (1977; Zbl 0355.34015)].
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Sturm-Liouville equations
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continuous spectra
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