Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions
Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symm...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/280970 |
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| _version_ | 1850219530565976064 |
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| author | Manfred Möller Bertin Zinsou |
| author_facet | Manfred Möller Bertin Zinsou |
| author_sort | Manfred Möller |
| collection | DOAJ |
| description | Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided. |
| format | Article |
| id | doaj-art-74bb5ce3e26d4b4881d367a52ba2b259 |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-74bb5ce3e26d4b4881d367a52ba2b2592025-08-20T02:07:20ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/280970280970Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary ConditionsManfred Möller0Bertin Zinsou1The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South AfricaThe John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South AfricaConsidered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.http://dx.doi.org/10.1155/2013/280970 |
| spellingShingle | Manfred Möller Bertin Zinsou Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions Journal of Function Spaces and Applications |
| title | Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions |
| title_full | Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions |
| title_fullStr | Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions |
| title_full_unstemmed | Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions |
| title_short | Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions |
| title_sort | asymptotics of the eigenvalues of a self adjoint fourth order boundary value problem with four eigenvalue parameter dependent boundary conditions |
| url | http://dx.doi.org/10.1155/2013/280970 |
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