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Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight

Author

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  • Ruyun Ma
  • Chenghua Gao
  • Yanqiong Lu

Abstract

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.

Suggested Citation

  • Ruyun Ma & Chenghua Gao & Yanqiong Lu, 2013. "Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, August.
    • Handle: RePEc:hin:jnlaaa:280508
    DOI: 10.1155/2013/280508
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