New Type of Sturm-Liouville Problems in Associated Hilbert Spaces
We introduce a new type of discontinuous Sturm-Liouville problems, involving an abstract linear operator in equation. By suggesting own approaches we define some new Hilbert spaces to establish such properties as isomorphism, coerciveness, and maximal decreasing of resolvent operator with respect to...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/606815 |
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| _version_ | 1832550295318560768 |
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| author | O. Sh. Mukhtarov K. Aydemir |
| author_facet | O. Sh. Mukhtarov K. Aydemir |
| author_sort | O. Sh. Mukhtarov |
| collection | DOAJ |
| description | We introduce a new type of discontinuous Sturm-Liouville problems, involving an abstract linear operator in equation. By suggesting own approaches we define some new Hilbert spaces to establish such properties as isomorphism, coerciveness, and maximal decreasing of resolvent operator with respect to spectral parameter. Then we find sufficient conditions for discreteness of the spectrum and examine asymptotic behaviour of eigenvalues. Obtained results are new even for continuous case, that is, without transmission conditions. |
| format | Article |
| id | doaj-art-9783ddfebaca4f909c1f5753ffa855a1 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9783ddfebaca4f909c1f5753ffa855a12025-02-03T06:07:14ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/606815606815New Type of Sturm-Liouville Problems in Associated Hilbert SpacesO. Sh. Mukhtarov0K. Aydemir1Department of Mathematics, Faculty of Science, Gaziosmanpaşa University, 60250 Tokat, TurkeyDepartment of Mathematics, Faculty of Science, Gaziosmanpaşa University, 60250 Tokat, TurkeyWe introduce a new type of discontinuous Sturm-Liouville problems, involving an abstract linear operator in equation. By suggesting own approaches we define some new Hilbert spaces to establish such properties as isomorphism, coerciveness, and maximal decreasing of resolvent operator with respect to spectral parameter. Then we find sufficient conditions for discreteness of the spectrum and examine asymptotic behaviour of eigenvalues. Obtained results are new even for continuous case, that is, without transmission conditions.http://dx.doi.org/10.1155/2014/606815 |
| spellingShingle | O. Sh. Mukhtarov K. Aydemir New Type of Sturm-Liouville Problems in Associated Hilbert Spaces Journal of Function Spaces |
| title | New Type of Sturm-Liouville Problems in Associated Hilbert Spaces |
| title_full | New Type of Sturm-Liouville Problems in Associated Hilbert Spaces |
| title_fullStr | New Type of Sturm-Liouville Problems in Associated Hilbert Spaces |
| title_full_unstemmed | New Type of Sturm-Liouville Problems in Associated Hilbert Spaces |
| title_short | New Type of Sturm-Liouville Problems in Associated Hilbert Spaces |
| title_sort | new type of sturm liouville problems in associated hilbert spaces |
| url | http://dx.doi.org/10.1155/2014/606815 |
| work_keys_str_mv | AT oshmukhtarov newtypeofsturmliouvilleproblemsinassociatedhilbertspaces AT kaydemir newtypeofsturmliouvilleproblemsinassociatedhilbertspaces |