Spectrum theory of second-order difference equations with indefinite weight

  • Ruyun Ma

    Northwest Normal University, Lanzhou, China
  • Chenghua Gao

    Northwest Normal University, Lanzhou, Gansu, China
  • Yanqiong Lu

    Northwest Normal University, Lanzhou, Gansu, China

Abstract

In this paper, we study the spectrum structure of second-order difference operators with sign-changing weight. We apply the Sylvester inertia theorem 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.

Cite this article

Ruyun Ma, Chenghua Gao, Yanqiong Lu, Spectrum theory of second-order difference equations with indefinite weight. J. Spectr. Theory 8 (2018), no. 3, pp. 971–985

DOI 10.4171/JST/219