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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 280508, 10 pages
http://dx.doi.org/10.1155/2013/280508
Research Article

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

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

Received 27 May 2013; Accepted 27 July 2013

Academic Editor: Yansheng Liu

Copyright © 2013 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

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.