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

Ruyun Ma | Zendy; Chenghua Gao | Zendy; Yanqiong Lu | Zendy

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

Author(s) -

Ruyun Ma,

Chenghua Gao,

Yanqiong Lu

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/280508

Subject(s) - eigenvalues and eigenvectors , sign (mathematics) , mathematics , weight function , spectrum (functional analysis) , eigenfunction , function (biology) , boundary (topology) , order (exchange) , value (mathematics) , combinatorics , mathematical analysis , statistics , physics , finance , quantum mechanics , evolutionary biology , economics , biology

We study the spectrum structure of discrete second-order Neumann boundary valueproblems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of theNBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues isequal to the number of positive elements in the weight function, and the number of negative eigenvaluesis equal to the number of negative elements in the weight function. We also show that the eigenfunctioncorresponding to the th positive/negative eigenvalue changes its sign exactly times

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