Eigenvalues of discrete Sturm–Liouville problems with eigenparameter dependent boundary conditions

Eigenvalues of discrete Sturm–Liouville problems with eigenparameter dependent boundary conditions We consider the discrete right definite Sturm–Liouville problems−Δ(p(t−1)Δy(t−1))+q(t)y(t)=λm(t)y(t),t∈[1,T]Z,(a0λ+b0)y(0)=(c0λ+d0)Δy(0),(a1λ+b1)y(T+1)=(c1λ+d1)∇y(T+1), where [1,T]Z={1,2,⋯,T}, m(t)>0 for t∈[1,T]Z, (−1)iδi≤0, where δi=aidi−bici for i=0,1. We obtain the existence of the eigenvalues, the sign-changing times of the eigenfunctions and the interlacing results of the eigenvalues of the above problem, the Dirichlet problem and the Neumann problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Linear Algebra and its Applications Elsevier

Eigenvalues of discrete Sturm–Liouville problems with eigenparameter dependent boundary conditions

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Publisher
Elsevier
Copyright
Copyright © 2016 Elsevier Inc.
ISSN
0024-3795
eISSN
1873-1856
D.O.I.
10.1016/j.laa.2016.03.043
Publisher site
See Article on Publisher Site

Abstract

We consider the discrete right definite Sturm–Liouville problems−Δ(p(t−1)Δy(t−1))+q(t)y(t)=λm(t)y(t),t∈[1,T]Z,(a0λ+b0)y(0)=(c0λ+d0)Δy(0),(a1λ+b1)y(T+1)=(c1λ+d1)∇y(T+1), where [1,T]Z={1,2,⋯,T}, m(t)>0 for t∈[1,T]Z, (−1)iδi≤0, where δi=aidi−bici for i=0,1. We obtain the existence of the eigenvalues, the sign-changing times of the eigenfunctions and the interlacing results of the eigenvalues of the above problem, the Dirichlet problem and the Neumann problem.

Journal

Linear Algebra and its ApplicationsElsevier

Published: Aug 15, 2016

References

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