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Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications

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  • Ruyun Ma
  • Man Xu
  • Yan Long

Abstract

Let be an integer and . We show the existence of the principal eigenvalues of linear periodic eigenvalue problem , and we determine the sign of the corresponding eigenfunctions, where is a parameter, and in , and the weight function changes its sign in . As an application of our spectrum results, we use the global bifurcation theory to study the existence of positive solutions for the corresponding nonlinear problem.

Suggested Citation

  • Ruyun Ma & Man Xu & Yan Long, 2018. "Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-8, January.
    • Handle: RePEc:hin:jnddns:1949254
    DOI: 10.1155/2018/1949254
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