Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse
In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equat...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/361989 |
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| author | Rauf Kh. Amırov A. Adiloglu Nabıev |
| author_facet | Rauf Kh. Amırov A. Adiloglu Nabıev |
| author_sort | Rauf Kh. Amırov |
| collection | DOAJ |
| description | In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved. |
| format | Article |
| id | doaj-art-39d07ed56d97444fba807e7dff93c775 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-39d07ed56d97444fba807e7dff93c7752025-02-03T01:22:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/361989361989Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with ImpulseRauf Kh. Amırov0A. Adiloglu Nabıev1Department of Mathematics, Faculty of Sciences, Cumhuriyet University, 58140 Sivas, TurkeyDepartment of Secondary Science and Mathematics Education, Faculty of Education, Cumhuriyet University, 58140 Sivas, TurkeyIn this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.http://dx.doi.org/10.1155/2013/361989 |
| spellingShingle | Rauf Kh. Amırov A. Adiloglu Nabıev Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse Abstract and Applied Analysis |
| title | Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse |
| title_full | Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse |
| title_fullStr | Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse |
| title_full_unstemmed | Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse |
| title_short | Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse |
| title_sort | inverse problems for the quadratic pencil of the sturm liouville equations with impulse |
| url | http://dx.doi.org/10.1155/2013/361989 |
| work_keys_str_mv | AT raufkhamırov inverseproblemsforthequadraticpencilofthesturmliouvilleequationswithimpulse AT aadiloglunabıev inverseproblemsforthequadraticpencilofthesturmliouvilleequationswithimpulse |