Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
We study the spectrum structure of discrete second-order Neumann boundary value problems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of the NBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues is equa...
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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/10.1155/2013/280508 |
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| _version_ | 1832548072606924800 |
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| author | Ruyun Ma Chenghua Gao Yanqiong Lu |
| author_facet | Ruyun Ma Chenghua Gao Yanqiong Lu |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | We study the spectrum structure of discrete second-order Neumann boundary value
problems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of the
NBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues is
equal to the number of positive elements in the weight function, and the number of negative eigenvalues
is equal to the number of negative elements in the weight function. We also show that the eigenfunction
corresponding to the th positive/negative eigenvalue changes its sign exactly times. |
| format | Article |
| id | doaj-art-a6002770647e45b7b92025d051d2c114 |
| 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-a6002770647e45b7b92025d051d2c1142025-02-03T06:42:23ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/280508280508Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing WeightRuyun Ma0Chenghua Gao1Yanqiong Lu2Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe study the spectrum structure of discrete second-order Neumann boundary value problems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of the NBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. We also show that the eigenfunction corresponding to the th positive/negative eigenvalue changes its sign exactly times.http://dx.doi.org/10.1155/2013/280508 |
| spellingShingle | Ruyun Ma Chenghua Gao Yanqiong Lu Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight Abstract and Applied Analysis |
| title | Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight |
| title_full | Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight |
| title_fullStr | Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight |
| title_full_unstemmed | Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight |
| title_short | Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight |
| title_sort | spectrum of discrete second order neumann boundary value problems with sign changing weight |
| url | http://dx.doi.org/10.1155/2013/280508 |
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