Spectrum of discrete second-order Neumann boundary value problems with sign-changing weight
type: Item
instance of: scholarly article
title: Spectrum of discrete second-order Neumann boundary value problems with sign-changing weight
zbMATH Open document ID: 1294.39002
DOI: 10.1155/2013/280508
author: Chenghua Gao
author: Yanqiong Lu
author: Ruyun Ma
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: 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 \(j\)th positive/negative eigenvalue changes its sign exactly \(j-1\) times.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 6306598
zbMATH Keywords: discrete second-order Neumann boundary value problems
zbMATH Keywords: sign-changing weight
zbMATH Keywords: characteristic determinant
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenfunction
Wikidata QID: Q58915795
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/280508
OpenAlex ID: W2042683126
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description: scientific article; zbMATH DE number 6306598