Article
| Title: | Green-Liouville approximation and correct solvability in $L_p(\mathbb R)$ of the general Sturm-Liouville equation (English) |
| Author: | Chernyavskaya, Nina |
| Author: | Shuster, Leonid |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 247-272 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We consider the equation $$ -(r(x) y'(x))'+q(x)y(x)=f(x),\quad x\in \mathbb R, $$ where $f\in L_p(\mathbb R)$, $p\in (1,\infty )$ and $$ r>0,\quad \frac {1}{r}\in L_1^{\rm loc}(\mathbb R),\quad q\in L_1^{\rm loc}(\mathbb R). $$ For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions $r$ and $q$ under which the above equation is correctly solvable in the space $L_p(\mathbb R),$ $p\in (1,\infty ).$ (English) |
| Keyword: | Green-Liouville approximation |
| Keyword: | correct solvability |
| Keyword: | general Sturm-Liouville equation |
| MSC: | 34B24 |
| MSC: | 34B27 |
| DOI: | 10.21136/CMJ.2024.0175-23 |
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| Date available: | 2024-03-13T10:09:19Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152278 |
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| Reference: | [8] Chernyavskaya, N. A., Shuster, L. A.: Methods of analysis of the condition for correct solvability in $L_p(\Bbb R)$ of general Sturm-Liouville equations.Czech. Math. J. 64 (2014), 1067-1098. Zbl 1349.34093, MR 3304799, 10.1007/s10587-014-0154-1 |
| Reference: | [9] Chernyavskaya, N., Shuster, L.: Criteria for correct solvability of a general Sturm-Liouville equation in the space $L_1(\Bbb R)$.Boll. Unione Mat. Ital. 11 (2018), 417-443. Zbl 1404.34019, MR 3869579, 10.1007/s40574-017-0144-y |
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