Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition
We consider the fourth-order spectral problem 𝑦(4)(𝑥)−(𝑞(𝑥)𝑦′(𝑥))=𝜆𝑦(𝑥),𝑥∈(0,𝑙) with spectral parameter in the boundary condition. We associate this problem with a selfadjoint operator in Hilbert or Pontryagin space. Using this operator-theoretic formulation and analytic methods, we investigate loc...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/456517 |
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| author | Ziyatkhan S. Aliyev Nazim B. Kerimov |
| author_facet | Ziyatkhan S. Aliyev Nazim B. Kerimov |
| author_sort | Ziyatkhan S. Aliyev |
| collection | DOAJ |
| description | We consider the fourth-order spectral problem 𝑦(4)(𝑥)−(𝑞(𝑥)𝑦′(𝑥))=𝜆𝑦(𝑥),𝑥∈(0,𝑙) with spectral parameter in the boundary condition. We associate this problem with a selfadjoint operator in Hilbert or Pontryagin space. Using this operator-theoretic formulation and analytic methods, we investigate locations (in complex plane) and multiplicities of the eigenvalues, the oscillation properties of the eigenfunctions, the basis properties in 𝐿𝑝(0,𝑙), 𝑝∈(1,∞), of the system of root functions of this problem. |
| format | Article |
| id | doaj-art-a54daad770b04a86b2159ac994a2ff19 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a54daad770b04a86b2159ac994a2ff192025-02-03T01:31:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/456517456517Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary ConditionZiyatkhan S. Aliyev0Nazim B. Kerimov1Department of Mathematics, Baku State University, Baku AZ 1148, AzerbaijanDepartment of Mathematics, Mersin University, 33343 Mersin, TurkeyWe consider the fourth-order spectral problem 𝑦(4)(𝑥)−(𝑞(𝑥)𝑦′(𝑥))=𝜆𝑦(𝑥),𝑥∈(0,𝑙) with spectral parameter in the boundary condition. We associate this problem with a selfadjoint operator in Hilbert or Pontryagin space. Using this operator-theoretic formulation and analytic methods, we investigate locations (in complex plane) and multiplicities of the eigenvalues, the oscillation properties of the eigenfunctions, the basis properties in 𝐿𝑝(0,𝑙), 𝑝∈(1,∞), of the system of root functions of this problem.http://dx.doi.org/10.1155/2012/456517 |
| spellingShingle | Ziyatkhan S. Aliyev Nazim B. Kerimov Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition International Journal of Mathematics and Mathematical Sciences |
| title | Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition |
| title_full | Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition |
| title_fullStr | Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition |
| title_full_unstemmed | Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition |
| title_short | Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition |
| title_sort | spectral properties of the differential operators of the fourth order with eigenvalue parameter dependent boundary condition |
| url | http://dx.doi.org/10.1155/2012/456517 |
| work_keys_str_mv | AT ziyatkhansaliyev spectralpropertiesofthedifferentialoperatorsofthefourthorderwitheigenvalueparameterdependentboundarycondition AT nazimbkerimov spectralpropertiesofthedifferentialoperatorsofthefourthorderwitheigenvalueparameterdependentboundarycondition |