On one boundary-value problem for elliptic differential-operator equations of the second order with quadratic spectral parameter
The problem of solvability of a boundary-value problem for a differential-operator equation of the second order on a finite interval is studied in a complex separable Hilbert space H in the case where the same spectral parameter appears in the equation in the form of a quadratic function and in the...
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| Datum: | 2017 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1732 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | The problem of solvability of a boundary-value problem for a differential-operator equation of the second order on a
finite interval is studied in a complex separable Hilbert space H in the case where the same spectral parameter appears
in the equation in the form of a quadratic function and in the boundary conditions in the form of a linear function and,
moreover, the boundary conditions are not separated. The asymptotic behavior of the eigenvalues of one homogeneous
abstract boundary-value problem is also investigated. The asymptotic formulas for the eigenvalues are obtained and an
application of the obtained results to partial differential equations is analyzed. |
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