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

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

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 equa...

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Main Authors: Ruyun Ma, Chenghua Gao, Yanqiong Lu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/280508
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spelling doaj-a6002770647e45b7b92025d051d2c1142020-11-24T22:51:49ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/280508280508Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing WeightRuyun Ma0Chenghua Gao1Yanqiong Lu2Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe 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.http://dx.doi.org/10.1155/2013/280508
collection DOAJ
language English
format Article
sources DOAJ
author Ruyun Ma
Chenghua Gao
Yanqiong Lu
spellingShingle Ruyun Ma
Chenghua Gao
Yanqiong Lu
Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
Abstract and Applied Analysis
author_facet Ruyun Ma
Chenghua Gao
Yanqiong Lu
author_sort Ruyun Ma
title Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
title_short Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
title_full Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
title_fullStr Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
title_full_unstemmed Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
title_sort spectrum of discrete second-order neumann boundary value problems with sign-changing weight
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/280508
work_keys_str_mv AT ruyunma spectrumofdiscretesecondorderneumannboundaryvalueproblemswithsignchangingweight
AT chenghuagao spectrumofdiscretesecondorderneumannboundaryvalueproblemswithsignchangingweight
AT yanqionglu spectrumofdiscretesecondorderneumannboundaryvalueproblemswithsignchangingweight
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