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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/280508 |
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |