On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem
An m-dimensional vectorial inverse nodal Sturm-Liouville problem with eigenparameter-dependent boundary conditions is studied. We show that if there exists an infinite sequence ynj,rx,λnj,r2j=1∞ of eigenfunctions which are all vectorial functions of type (CZ), then the potential matrix Qx and A are...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6953602 |
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| _version_ | 1832556816574185472 |
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| author | Xiaoyun Liu |
| author_facet | Xiaoyun Liu |
| author_sort | Xiaoyun Liu |
| collection | DOAJ |
| description | An m-dimensional vectorial inverse nodal Sturm-Liouville problem with eigenparameter-dependent boundary conditions is studied. We show that if there exists an infinite sequence ynj,rx,λnj,r2j=1∞ of eigenfunctions which are all vectorial functions of type (CZ), then the potential matrix Qx and A are simultaneously diagonalizable by the same unitary matrix U. Subsequently, some multiplicity results of eigenvalues are obtained. |
| format | Article |
| id | doaj-art-5d3ecfc075ec4905a62ad045ac946b20 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5d3ecfc075ec4905a62ad045ac946b202025-02-03T05:44:21ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/69536026953602On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville ProblemXiaoyun Liu0School of Mathematics and Physics, Anyang Institute of Technology, Anyang, 455000 Henan, ChinaAn m-dimensional vectorial inverse nodal Sturm-Liouville problem with eigenparameter-dependent boundary conditions is studied. We show that if there exists an infinite sequence ynj,rx,λnj,r2j=1∞ of eigenfunctions which are all vectorial functions of type (CZ), then the potential matrix Qx and A are simultaneously diagonalizable by the same unitary matrix U. Subsequently, some multiplicity results of eigenvalues are obtained.http://dx.doi.org/10.1155/2020/6953602 |
| spellingShingle | Xiaoyun Liu On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem Journal of Function Spaces |
| title | On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem |
| title_full | On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem |
| title_fullStr | On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem |
| title_full_unstemmed | On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem |
| title_short | On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem |
| title_sort | on inverse nodal problem and multiplicities of eigenvalues of a vectorial sturm liouville problem |
| url | http://dx.doi.org/10.1155/2020/6953602 |
| work_keys_str_mv | AT xiaoyunliu oninversenodalproblemandmultiplicitiesofeigenvaluesofavectorialsturmliouvilleproblem |