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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 1949254, 8 pages
https://doi.org/10.1155/2018/1949254
Research Article

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

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Correspondence should be addressed to Ruyun Ma; nc.ude.unwn@yram

Received 31 October 2017; Revised 14 December 2017; Accepted 24 December 2017; Published 18 January 2018

Academic Editor: Douglas R. Anderson

Copyright © 2018 Ruyun Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.