A note on Sturm-Liouville problems whose spectrum is the set of prime numbers
We show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book [9]. We also show that there may exist such a problem if...
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| Format: | Article |
| Language: | English |
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Texas State University
2011-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/123/abstr.html |
| _version_ | 1818927472304979968 |
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| author | Angelo B. Mingarelli |
| author_facet | Angelo B. Mingarelli |
| author_sort | Angelo B. Mingarelli |
| collection | DOAJ |
| description | We show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book [9]. We also show that there may exist such a problem if the parameter dependence is nonlinear. |
| first_indexed | 2024-12-20T03:13:33Z |
| format | Article |
| id | doaj.art-6ca76c15cfb74579aafb5812342d8bde |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T03:13:33Z |
| publishDate | 2011-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-6ca76c15cfb74579aafb5812342d8bde2022-12-21T19:55:24ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-09-012011123,14A note on Sturm-Liouville problems whose spectrum is the set of prime numbersAngelo B. MingarelliWe show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book [9]. We also show that there may exist such a problem if the parameter dependence is nonlinear.http://ejde.math.txstate.edu/Volumes/2011/123/abstr.htmlSturm-Liouvillespectrumprime numbers |
| spellingShingle | Angelo B. Mingarelli A note on Sturm-Liouville problems whose spectrum is the set of prime numbers Electronic Journal of Differential Equations Sturm-Liouville spectrum prime numbers |
| title | A note on Sturm-Liouville problems whose spectrum is the set of prime numbers |
| title_full | A note on Sturm-Liouville problems whose spectrum is the set of prime numbers |
| title_fullStr | A note on Sturm-Liouville problems whose spectrum is the set of prime numbers |
| title_full_unstemmed | A note on Sturm-Liouville problems whose spectrum is the set of prime numbers |
| title_short | A note on Sturm-Liouville problems whose spectrum is the set of prime numbers |
| title_sort | note on sturm liouville problems whose spectrum is the set of prime numbers |
| topic | Sturm-Liouville spectrum prime numbers |
| url | http://ejde.math.txstate.edu/Volumes/2011/123/abstr.html |
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